{"id":715,"date":"2023-07-29T00:10:17","date_gmt":"2023-07-29T00:10:17","guid":{"rendered":"https:\/\/statorials.org\/my\/binomial-%e1%80%96%e1%80%bc%e1%80%94%e1%80%b7%e1%80%ba%e1%80%96%e1%80%bc%e1%80%b0%e1%80%b8%e1%80%81%e1%80%bc%e1%80%84%e1%80%ba%e1%80%b8%e1%81%8b\/"},"modified":"2023-07-29T00:10:17","modified_gmt":"2023-07-29T00:10:17","slug":"binomial-%e1%80%96%e1%80%bc%e1%80%94%e1%80%b7%e1%80%ba%e1%80%96%e1%80%bc%e1%80%b0%e1%80%b8%e1%80%81%e1%80%bc%e1%80%84%e1%80%ba%e1%80%b8%e1%81%8b","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/binomial-%e1%80%96%e1%80%bc%e1%80%94%e1%80%b7%e1%80%ba%e1%80%96%e1%80%bc%e1%80%b0%e1%80%b8%e1%80%81%e1%80%bc%e1%80%84%e1%80%ba%e1%80%b8%e1%81%8b\/","title":{"rendered":"Binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1014\u102d\u1012\u102b\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u102f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>#words {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#words label, input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;\n      padding: 10px 10px;\n      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #button:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>p, li {\n  color:#000000;\n  font-size: 19px;\n  font-family: 'Helvetica';\n}<\/p>\n<p>p a {\n  color: #9b59b6 !important;\n}\n<\/style>\n<p class=\"has-text-color\" style=\"color:#000000\"><strong>binomial distribution<\/strong> \u101e\u100a\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u101b\u1031\u1015\u1014\u103a\u1038\u1021\u1005\u102c\u1038\u1006\u102f\u1036\u1038 \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/binomial-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"binomial experiments (opens in a new tab)\">binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/a> \u1026\u1038\u1005\u103d\u102c\u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a \u1000\u1030\u100a\u102e\u1015\u1031\u1038\u101e\u100a\u103a\u104b<\/p>\n<h3 class=\"wp-block-heading\"> <strong>Binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038<\/strong><\/h3>\n<p> <strong>binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103b\u1000\u103a<\/strong> \u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1002\u102f\u100f\u103a\u101e\u1010\u1039\u1010\u102d\u1019\u103b\u102c\u1038\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/p>\n<ul>\n<li> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a <em>\u1011\u1015\u103a\u1001\u102b\u1010\u101c\u1032\u101c\u1032<\/em> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1015\u102b\u101d\u1004\u103a\u101e\u100a\u103a\u104b<\/li>\n<li> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103b\u1031\u101b\u101c\u1012\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u102c\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/li>\n<li> <em>\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/em> \u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u100a\u103a\u104b<\/li>\n<li> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<\/ul>\n<p> binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f \u1021\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1006\u102f\u1036\u1038 \u1025\u1015\u1019\u102c\u1019\u103e\u102c \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1015\u1005\u103a\u1001\u103c\u1004\u103a\u1038 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c\u104a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1000\u102d\u102f \u1041\u1040 \u1000\u103c\u102d\u1019\u103a\u101c\u103e\u1014\u103a\u1010\u101a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1002\u102f\u100f\u103a\u101e\u1010\u1039\u1010\u102d\u101c\u1031\u1038\u1001\u102f\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u104e\u1004\u103a\u1038\u1010\u103d\u1004\u103a binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/p>\n<ul>\n<li> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a <em>\u1011\u1015\u103a\u1001\u102b\u1010\u101c\u1032\u101c\u1032<\/em> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1015\u102b\u101d\u1004\u103a\u101e\u100a\u103a &#8211; \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f 10 \u1001\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/li>\n<li> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101b\u103e\u102d\u101e\u1031\u102c \u101b\u101c\u1012\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u102c\u101b\u103e\u102d\u101e\u100a\u103a- \u1026\u1038\u1001\u1031\u102b\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u1019\u103c\u102e\u1038\u1019\u103b\u102c\u1038\u104b<\/li>\n<li> <em>\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/em> \u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u100a\u103a\u104b \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a &#8220; \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f&#8221;  \u1000\u102d\u102f \u1006\u1004\u103a\u1038\u101e\u1000\u103a\u101e\u100a\u1037\u103a \u1026\u1038\u1001\u1031\u102b\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1021\u1016\u103c\u1005\u103a \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u1000\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a 0.5 \u1021\u1010\u102d\u1021\u1000\u103b\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<li> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a- \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1010\u1005\u103a\u1001\u102f\u1015\u1005\u103a\u1001\u103c\u1004\u103a\u1038\u104f\u101b\u101c\u1012\u103a\u101e\u100a\u103a \u1021\u1001\u103c\u102c\u1038\u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1015\u1005\u103a\u1001\u103c\u1004\u103a\u1038\u104f\u101b\u101c\u1012\u103a\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> <strong>binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f<\/strong><\/h3>\n<p> <strong>binomial distribution \u101e\u100a\u103a<\/strong> <em>n<\/em> binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a <em>k<\/em> \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u101b\u101b\u103e\u102d\u101b\u1014\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/\u1000\u103b\u1015\u1014\u103a\u1038-\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"random variable (opens in a new tab)\">\u1000\u103b\u1015\u1014\u103a\u1038 variable<\/a> <em>X \u101e\u100a\u103a<\/em> binomial distribution \u1000\u102d\u102f \u101c\u102d\u102f\u1000\u103a\u1014\u102c\u1015\u102b\u1000\u104a <em>X<\/em> = <em>k<\/em> \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u102c\u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/p>\n<p> <strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/p>\n<p> \u101b\u103d\u103e\u1031-<\/p>\n<ul>\n<li> <strong>n:<\/strong> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/li>\n<li> <strong>k:<\/strong> \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/li>\n<li> <strong>p-<\/strong> \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031<\/li>\n<li> <strong><sub>n<\/sub> C <sub>k<\/sub> :<\/strong> <em>n<\/em> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a <em>k<\/em> \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101b\u101b\u103e\u102d\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038<\/li>\n<\/ul>\n<p> \u1025\u1015\u1019\u102c\u104a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1000\u102d\u102f \u1043 \u1000\u103c\u102d\u1019\u103a\u101c\u103e\u1014\u103a\u1010\u101a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1024 3 \u1000\u103c\u102d\u1019\u103a\u1010\u103d\u1004\u103a 0\u104a 1\u104a 2 \u1014\u103e\u1004\u1037\u103a 3 \u1001\u1031\u102b\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u101a\u1030\u101b\u1014\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u1011\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<p> <strong>P(X=0)<\/strong> = <sub>3<\/sub> C <sub>0<\/sub> * 0.5 <sup>0<\/sup> * (1-0.5) <sup>3-0<\/sup> = 1 * 1 * (0.5) <sup>3<\/sup> = <strong>0.125\u104a<\/strong><\/p>\n<p> <strong>P(X=1)<\/strong> = <sub>3<\/sub> C <sub>1<\/sub> * 0.5 <sup>1<\/sup> * (1-0.5) <sup>3-1<\/sup> = 3 * 0.5 * (0.5) <sup>2<\/sup> = <strong>0.375\u104a<\/strong><\/p>\n<p> <strong>P(X=2)<\/strong> = <sub>3<\/sub> C <sub>2<\/sub> * 0.5 <sup>2<\/sup> * (1-0.5) <sup>3-2<\/sup> = 3 * 0.25 * (0.5) <sup>1<\/sup> = <strong>0.375\u104a<\/strong><\/p>\n<p> <strong>P(X=3)<\/strong> = <sub>3<\/sub> C <sub>3<\/sub> * 0.5 <sup>3<\/sup> * (1-0.5) <sup>3-3<\/sup> = 1 * 0.125 * (0.5) <sup>0<\/sup> = <strong>0.125\u104a<\/strong><\/p>\n<p> <em>\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a<\/em> <strong><em>&#8211;<\/em><\/strong> <em>\u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1005\u102e<\/em> <sub><em>\u1021\u1010\u103d\u1000\u103a<\/em><\/sub> <sub><em>nCk \u1000\u102d\u102f<\/em><\/sub> <em>\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1024 <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Combination Calculator (opens in a new tab)\">\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a\u1000\u102d\u102f<\/a> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u1032\u1037\u101e\u100a\u103a<\/em> \u104b<\/p>\n<p> \u1024\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103b\u1031 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u101f\u102e\u1005\u1010\u102d\u102f\u1002\u101b\u1019\u103a\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a- <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomdist1.png\" alt=\"Binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u101b\u1031\u1038 \u101f\u1005\u103a\u1005\u1010\u102d\u102f\u1002\u101b\u1019\u103a\" class=\"wp-image-7153\" width=\"339\" height=\"335\" srcset=\"\" sizes=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> <strong>\u1010\u102d\u102f\u1038\u1015\u103d\u102c\u1038\u101c\u102c\u101e\u1031\u102c binomial \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u104b<\/strong><\/h3>\n<p> \u1021\u1011\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d binomial probability \u1010\u1005\u103a\u1001\u102f\u1010\u100a\u103a\u1038 (\u1025\u1015\u1019\u102c- \u1012\u1004\u103a\u1039\u1002\u102b\u1038\u1010\u1005\u103a\u1015\u103c\u102c\u1038\u104f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a \u1021\u1011\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1015\u102f\u1036\u101e\u1031\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037 \u1043 \u1000\u103c\u102d\u1019\u103a\u1019\u103e \u1041 \u1000\u103c\u102d\u1019\u103a) \u1015\u1031\u102b\u103a\u101c\u102c\u1014\u102d\u102f\u1004\u103a\u1001\u103b\u1031\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038\u104a \u1010\u102d\u102f\u1038\u1015\u103d\u102c\u1038\u101c\u102c\u101e\u1031\u102c binomial \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u1005\u103a\u1026\u1038\u1001\u103b\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103b\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u1031\u102b\u1004\u103a\u1038\u1011\u100a\u1037\u103a\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<p> \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037 \u1043 \u1000\u103c\u102d\u1019\u103a\u1019\u103e \u1041 \u1000\u103c\u102d\u1019\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u1012\u1004\u103a\u1039\u1002\u102b\u1038\u1015\u103c\u102c\u1038\u1010\u1005\u103a\u1001\u102f \u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a\u1010\u1000\u103a\u101c\u102c\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101e\u102d\u1001\u103b\u1004\u103a\u101e\u100a\u103a\u1006\u102d\u102f\u1000\u103c\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1024\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/p>\n<p> <strong>P(X\u22641)<\/strong> = P(X=0) + P(X=1) = 0.125 + 0.375 = <strong>0.5<\/strong> \u104b<\/p>\n<p> \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u1000\u102d\u102f \u1015\u1031\u102b\u1004\u103a\u1038\u1011\u100a\u1037\u103a\u1001\u103c\u1004\u103a\u1038\u1010\u102d\u102f\u1037 \u1015\u102b\u101d\u1004\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u104e\u1004\u103a\u1038\u1000\u102d\u102f <strong>\u1005\u102f\u1006\u1031\u102c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031<\/strong> \u101f\u102f \u1001\u1031\u102b\u103a\u101e\u100a\u103a\u104b \u1021\u101c\u102c\u1038\u1010\u1030 \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u101b\u101c\u1012\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a <em>k<\/em> \u1026\u1038\u1001\u1031\u102b\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u101b\u101b\u103e\u102d\u1001\u103c\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1015\u102d\u102f\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/p>\n<p> <strong>P(X\u22640)<\/strong> = P(X=0) = <strong>0.125<\/strong> \u104b<\/p>\n<p> <strong>P(X\u22641)<\/strong> = P(X=0) + P(X=1) = 0.125 + 0.375 = <strong>0.5<\/strong> \u104b<\/p>\n<p> <strong>P(X\u22642)<\/strong> = P(X=0) + P(X=1) + P(X=2) = 0.125 + 0.375 + 0.375 = <strong>0.875<\/strong> \u104b<\/p>\n<p> <strong>P(X\u22643)<\/strong> = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.125 + 0.375 + 0.375 + 0.125 = <strong>1<\/strong> \u104b<\/p>\n<p> \u1024\u1005\u102f\u1005\u100a\u103a\u1038\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u101f\u102e\u1005\u1010\u102d\u102f\u1002\u101b\u1019\u103a\u1010\u1005\u103a\u1001\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a- <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomdist2.png\" alt=\"\u1005\u102f\u1005\u100a\u103a\u1038\u1019\u103e\u102f binomial \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\" class=\"wp-image-7161\" width=\"346\" height=\"341\" srcset=\"\" sizes=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> <strong>Binomial Probability \u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a<\/strong><\/h3>\n<p> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u101e\u1031\u102c \u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u101c\u102f\u1015\u103a\u101c\u102f\u1015\u103a\u101e\u1031\u102c\u1021\u1001\u102b (\u1025\u1015\u1019\u102c- \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037 3 \u1015\u103c\u102c\u1038\u1000\u102d\u102f \u101c\u103d\u103e\u1004\u1037\u103a\u1015\u1005\u103a\u1001\u103c\u1004\u103a\u1038) \u101e\u100a\u103a binomial \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u1000\u103a\u1016\u103c\u1004\u1037\u103a \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1000\u103b\u102d\u102f\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1006\u102e\u101c\u103b\u1031\u102c\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u102d\u102f\u1000\u103c\u102e\u1038\u101e\u1031\u102c \u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u101c\u102f\u1015\u103a\u101c\u102f\u1015\u103a\u101e\u1031\u102c\u1021\u1001\u102b (\u1025\u1015\u1019\u102c 100 \u101e\u101b\u1031\u1000\u103b\u1001\u103c\u1004\u103a\u1038)\u104a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u1000\u103a\u1016\u103c\u1004\u1037\u103a \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1001\u1000\u103a\u1001\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1024\u1000\u102d\u1005\u1039\u1005\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1000\u1032\u1037\u101e\u102d\u102f\u1037 <strong>binomial probability calculator \u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1021\u1011\u1031\u102c\u1000\u103a\u1021\u1000\u1030\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/p>\n<p> \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037 n = 100 \u1000\u103c\u102d\u1019\u103a \u1015\u1005\u103a\u1001\u103b\u101c\u102d\u102f\u1000\u103a\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1026\u1038\u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a\u1010\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u104f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c p = 0.5 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a k = 43 \u1000\u103c\u102d\u1019\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u101e\u102d\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<div id=\"words\"> <label for=\"p\"><b>p<\/b> (\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031)<\/label><input id=\"p\" min=\"0\" type=\"number\" value=\"0.5\"><\/div>\n<div id=\"words\"> <label for=\"n\"><b>n<\/b> (\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a)<\/label><input id=\"n\" min=\"0\" type=\"number\" value=\"100\"><\/div>\n<div id=\"words\"> <label for=\"k\"><b>k<\/b> (\u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a)<\/label> <input id=\"k\" min=\"0\" type=\"number\" value=\"43\"><\/div>\n<div id=\"words\"><input id=\"button\" type=\"button\" value=\"Calculate\" onclick=\"pvalue()\"><\/div>\n<div id=\"words\">\n<p> P(X= <span id=\"k1\">43<\/span> ) = <span id=\"exactProb\">0.03007<\/span><\/p>\n<p> P(X&lt; <span id=\"k2\">43<\/span> ) = <span id=\"lessProb\">0.06661<\/span><\/p>\n<p> P( <span id=\"k3\">X\u226443<\/span> ) = <span id=\"lessEProb\">0.09667<\/span><\/p>\n<p> P(X&gt; <span id=\"k4\">43<\/span> ) = <span id=\"greaterProb\">0.90333<\/span><\/p>\n<p> P( <span id=\"k5\">X\u226543<\/span> ) = <span id=\"greaterEProb\">0.93339<\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>function pvalue() {<\/p>\n<p>\/\/get input values\nvar p = document.getElementById('p').value*1;\nvar n = document.getElementById('n').value*1;\nvar k = document.getElementById('k').value*1;<\/p>\n<p>\/\/assign probabilities to variable names\nvar exactProb = jStat.binomial.pdf(k,n,p);\nvar lessProb = jStat.binomial.cdf(k-1,n,p);\nvar lessEProb = jStat.binomial.cdf(k,n,p);\nvar greaterProb = 1-jStat.binomial.cdf(k,n,p);\nvar greaterEProb = 1-jStat.binomial.cdf(k-1,n,p);<\/p>\n<p>\/\/output probabilities\ndocument.getElementById('k1').innerHTML = k;\ndocument.getElementById('k2').innerHTML = k;\ndocument.getElementById('k3').innerHTML = k;\ndocument.getElementById('k4').innerHTML = k;\ndocument.getElementById('k5').innerHTML = k;<\/p>\n<p>document.getElementById('exactProb').innerHTML = exactProb.toFixed(5);\ndocument.getElementById('lessProb').innerHTML = lessProb.toFixed(5);\ndocument.getElementById('lessEProb').innerHTML = lessEProb.toFixed(5);\ndocument.getElementById('greaterProb').innerHTML = greaterProb.toFixed(5);\ndocument.getElementById('greaterEProb').innerHTML = greaterEProb.toFixed(5);\n}\n<\/script><\/p>\n<p>\u1024\u101e\u100a\u103a\u1019\u103e\u102c \u101b\u101c\u1012\u103a\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/p>\n<ul>\n<li> \u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a\u1010\u1000\u103a\u101c\u102c\u101e\u1031\u102c \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u104f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a 43 \u1000\u103c\u102d\u1019\u103a\u1010\u102d\u1010\u102d <strong>0.03007<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<li> 43 \u1000\u103c\u102d\u1019\u103a\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c\u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1019\u103b\u102c\u1038\u104f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a <strong>0.06661<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<li> 43 \u1000\u103c\u102d\u1019\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u1012\u1004\u103a\u1039\u1002\u102b\u1038\u1015\u103c\u102c\u1038\u104f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a <strong>0.09667<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<li> \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a\u1010\u1000\u103a\u101c\u102c\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 43 \u1000\u103c\u102d\u1019\u103a\u1011\u1000\u103a <strong>0.90333<\/strong> \u1016\u103c\u1005\u103a\u1015\u102b\u1010\u101a\u103a\u104b<\/li>\n<li> \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037 \u1044\u1043 \u1000\u103c\u102d\u1019\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1037\u1011\u1000\u103a\u1015\u102d\u102f\u104d \u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a\u1010\u1000\u103a\u101c\u102c\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c <strong>0.93339<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> <strong>binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1001\u103c\u1004\u103a\u1038\u104f \u1002\u102f\u100f\u103a\u101e\u1010\u1039\u1010\u102d\u1019\u103b\u102c\u1038<\/strong><\/h3>\n<p> binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1002\u102f\u100f\u103a\u101e\u1010\u1039\u1010\u102d\u1019\u103b\u102c\u1038 \u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/p>\n<p> \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1019\u103e\u102c <strong>\u03bc = np<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/p>\n<p> \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u104f\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101e\u100a\u103a <strong>\u03c3<\/strong> <sup><strong>2<\/strong><\/sup> <strong>= np(1-p)<\/strong><\/p>\n<p> \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1019\u103e\u102c <strong>\u03c3 = \u221a<\/strong> <span style=\"text-decoration: overline;\"><strong>np(1-p)<\/strong><\/span> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/p>\n<p> \u1025\u1015\u1019\u102c\u104a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1000\u102d\u102f \u1043 \u1000\u103c\u102d\u1019\u103a\u101c\u1031\u102c\u1000\u103a \u1015\u1005\u103a\u1010\u101a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b p = \u1012\u1004\u103a\u1039\u1002\u102b\u1038\u1015\u103c\u102c\u1038\u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a\u1000\u103b\u101e\u1031\u102c \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/p>\n<p> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1019\u103b\u103e\u1031\u102c\u103a\u101c\u1004\u1037\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1026\u1038\u1001\u1031\u102b\u1004\u103a\u1038\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1019\u103e\u102c \u03bc = np = 3*.5 = <strong>1.5<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/p>\n<p> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1019\u103b\u103e\u1031\u102c\u103a\u101c\u1004\u1037\u103a\u1011\u102c\u1038\u101e\u1031\u102c head count varianance \u101e\u100a\u103a \u03c3 <sup>2<\/sup> = np(1-p) = 3*.5*(1-.5) = <strong>0.75 \u1016\u103c\u1005\u103a\u101e\u100a\u103a<\/strong> \u104b<\/p>\n<h3 class=\"wp-block-heading\"> <strong>Binomial Distribution Practice \u1015\u103c\u103f\u1014\u102c\u1019\u103b\u102c\u1038<\/strong><\/h3>\n<p> binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1001\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u1004\u103a\u104f\u1021\u101e\u102d\u1015\u100a\u102c\u1000\u102d\u102f \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u101c\u1031\u1037\u1021\u1000\u103b\u1004\u1037\u103a\u1015\u103c\u103f\u1014\u102c\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u104b<\/p>\n<p> <strong>\u1015\u103c\u103f\u1014\u102c \u1041<\/strong><\/p>\n<p> <strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> Bob \u101e\u100a\u103a \u101e\u1030\u104f \u1021\u101c\u103d\u1010\u103a\u1015\u1005\u103a\u101b\u1014\u103a \u1000\u103c\u102d\u102f\u1038\u1005\u102c\u1038\u1019\u103e\u102f 60% \u1000\u102d\u102f \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101e\u100a\u103a\u104b \u1021\u1000\u101a\u103a\u104d \u101e\u1030\u101e\u100a\u103a \u1021\u101c\u103d\u1010\u103a\u1015\u1005\u103a\u1001\u103b\u1000\u103a 12 \u1000\u103c\u102d\u1019\u103a\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1015\u102b\u1000\u104a \u101e\u1030 10 \u1010\u102d\u1010\u102d\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c \u1021\u1018\u101a\u103a\u1014\u100a\u103a\u1038\u104b<\/p>\n<p> <strong>\u1021\u1016\u103c\u1031-<\/strong> p = 0.6\u104a n = 12 \u1014\u103e\u1004\u1037\u103a k = 10 \u1016\u103c\u1004\u1037\u103a \u1021\u1011\u1000\u103a\u1010\u103d\u1004\u103a\u101b\u103e\u102d\u101e\u1031\u102c binomial distribution calculator \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d P(X=10) = <strong>0.06385<\/strong> \u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1010\u103d\u1031\u1037\u101b\u103e\u102d\u101b\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<p> <strong>\u1015\u103c\u103f\u1014\u102c \u1042<\/strong><\/p>\n<p> <strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> Jessica \u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1000\u102d\u102f \u1045 \u1000\u103c\u102d\u1019\u103a\u101c\u103e\u1014\u103a\u101e\u100a\u103a\u104b \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037 \u1042 \u1000\u103c\u102d\u1019\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1019\u103b\u102c\u1038 \u1001\u1031\u102b\u1004\u103a\u1038\u1015\u1031\u102b\u103a\u1010\u1000\u103a\u101c\u102c\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1019\u100a\u103a\u1019\u103b\u103e\u101b\u103e\u102d\u101e\u1014\u100a\u103a\u1038\u104b<\/p>\n<p> <strong>\u1021\u1016\u103c\u1031-<\/strong> p = 0.5\u104a n = 5 \u1014\u103e\u1004\u1037\u103a k = 2 \u1016\u103c\u1004\u1037\u103a \u1021\u1011\u1000\u103a\u1010\u103d\u1004\u103a\u101b\u103e\u102d\u101e\u1031\u102c binomial distribution calculator \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d P(X\u22642) = <strong>0.5<\/strong> \u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<p> <strong>\u1015\u103c\u103f\u1014\u102c \u1043<\/strong><\/p>\n<p> <strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u102c\u1038 \u1000\u1031\u102c\u101c\u102d\u1015\u103a\u1010\u1005\u103a\u1001\u102f\u101e\u102d\u102f\u1037 \u101c\u1000\u103a\u1001\u1036\u1019\u100a\u1037\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c 0.2 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 10 \u1026\u1038 \u101c\u103b\u103e\u1031\u102c\u1000\u103a\u1011\u102c\u1038\u1015\u102b\u1000 4 \u1026\u1038\u1011\u1000\u103a\u1015\u102d\u102f\u101c\u1000\u103a\u1001\u1036\u1019\u100a\u1037\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1019\u100a\u103a\u1019\u103b\u103e\u101b\u103e\u102d\u101e\u1014\u100a\u103a\u1038\u104b<\/p>\n<p> <strong>\u1021\u1016\u103c\u1031-<\/strong> p = 0.2\u104a n = 10 \u1014\u103e\u1004\u1037\u103a k = 4 \u1016\u103c\u1004\u1037\u103a \u1021\u1011\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b binomial distribution calculator \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d P(X&gt;4) = <strong>0.03279<\/strong> \u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<p> <strong>\u1015\u103c\u103f\u1014\u102c \u1044<\/strong><\/p>\n<p> <strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> \u101e\u1004\u103a\u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1000\u102d\u102f \u1041\u1042 \u1000\u103c\u102d\u1019\u103a\u101c\u103e\u1014\u103a\u1015\u102b\u104b \u1015\u1031\u102b\u103a\u101c\u102c\u1019\u100a\u1037\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1026\u1038\u1001\u1031\u102b\u1004\u103a\u1038\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1000 \u1018\u101a\u103a\u101c\u1031\u102c\u1000\u103a\u101c\u1032\u104b<\/p>\n<p> <strong>\u1021\u1016\u103c\u1031-<\/strong> binomial distribution \u1010\u1005\u103a\u1001\u102f\u104f \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1000\u102d\u102f \u03bc = np \u1021\u1016\u103c\u1005\u103a \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1011\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1019\u103e\u1010\u103a\u101e\u102c\u1038\u1015\u102b\u104b \u1012\u102e\u1010\u1031\u102c\u1037 \u03bc = 12*0.5 = <strong>6 \u1001\u1031\u102b\u1004\u103a\u1038<\/strong> \u104b<\/p>\n<p> <strong>\u1015\u103c\u103f\u1014\u102c \u1045<\/strong><\/p>\n<p> <strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> Mark \u101e\u100a\u103a \u101e\u1030\u1000\u103c\u102d\u102f\u1038\u1005\u102c\u1038\u1019\u103e\u102f\u104f 10% \u1016\u103c\u1004\u1037\u103a \u1021\u102d\u1019\u103a\u1015\u103c\u1014\u103a\u1015\u103c\u1031\u1038\u1001\u103c\u1004\u103a\u1038 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u101e\u1030\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u1002\u102d\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a 5 \u1000\u103c\u102d\u1019\u103a\u1000\u103c\u102d\u102f\u1038\u1005\u102c\u1038\u1015\u102b\u1000\u104a \u101e\u1030\u1010\u102d\u102f\u1000\u103a\u1019\u102d\u101e\u100a\u1037\u103a\u1021\u102d\u1019\u103a\u1000\u103d\u1004\u103a\u1038\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103e\u102c \u1021\u1018\u101a\u103a\u1014\u100a\u103a\u1038\u104b<\/p>\n<p> <strong>\u1021\u1016\u103c\u1031-<\/strong> binomial distribution \u1010\u1005\u103a\u1001\u102f\u104f \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u03c3 <sup>2<\/sup> = np(1-p) \u1021\u1016\u103c\u1005\u103a \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1011\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u102d\u101b\u1015\u102b\u104b \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a <sup>\u03c32<\/sup> = 6*.1*(1-.1) = <strong>0.54<\/strong> \u104b<\/p>\n<h3 class=\"wp-block-heading\"> <strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/h3>\n<p> \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1006\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u1031\u102c\u1037\u1016\u103a\u101d\u1032\u101c\u103a\u1010\u103d\u1004\u103a binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u101c\u1031\u1037\u101c\u102c\u101b\u1014\u103a \u1000\u1030\u100a\u102e\u1015\u1031\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/my\/binomial-distribution-excel\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities in Excel (opens in a new tab)\">Excel \u1010\u103d\u1004\u103a Binomial Probabilities \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u100a\u103a\u1038<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/my\/binomial-probabilities-ti-84-\u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities on a TI-84 calculator (opens in a new tab)\">TI-84 \u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a\u1010\u103d\u1004\u103a Binomial Probabilities \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u100a\u103a\u1038<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noreferrer noopener\">R \u1010\u103d\u1004\u103a binomial probabilities \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u100a\u103a\u1038<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/my\/binomial-distribution-r-\u1000\u102d\u102f-\u1000\u103c\u1036\u1005\u100a\u103a\u1015\u102b\u104b\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to plot a binomial distribution in R (opens in a new tab)\">R \u1010\u103d\u1004\u103a binomial \u1016\u103c\u1014\u1037\u103a\u1001\u103b\u102e\u1015\u102f\u1036\u1006\u103d\u1032\u1014\u100a\u103a\u1038<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>binomial distribution \u101e\u100a\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u101b\u1031\u1015\u1014\u103a\u1038\u1021\u1005\u102c\u1038\u1006\u102f\u1036\u1038 \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1026\u1038\u1005\u103d\u102c\u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a \u1000\u1030\u100a\u102e\u1015\u1031\u1038\u101e\u100a\u103a\u104b Binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103b\u1000\u103a \u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1002\u102f\u100f\u103a\u101e\u1010\u1039\u1010\u102d\u1019\u103b\u102c\u1038\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1011\u1015\u103a\u1001\u102b\u1010\u101c\u1032\u101c\u1032 \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1015\u102b\u101d\u1004\u103a\u101e\u100a\u103a\u104b \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103b\u1031\u101b\u101c\u1012\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u102c\u101b\u103e\u102d\u101e\u100a\u103a\u104b \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u100a\u103a\u104b \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f \u1021\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1006\u102f\u1036\u1038 \u1025\u1015\u1019\u102c\u1019\u103e\u102c \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1015\u1005\u103a\u1001\u103c\u1004\u103a\u1038 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c\u104a \u1021\u1000\u103c\u103d\u1031\u1005\u1031\u1037\u1000\u102d\u102f \u1041\u1040 \u1000\u103c\u102d\u1019\u103a\u101c\u103e\u1014\u103a\u1010\u101a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1002\u102f\u100f\u103a\u101e\u1010\u1039\u1010\u102d\u101c\u1031\u1038\u1001\u102f\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u104e\u1004\u103a\u1038\u1010\u103d\u1004\u103a binomial \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1011\u1015\u103a\u1001\u102b\u1010\u101c\u1032\u101c\u1032 \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1015\u102b\u101d\u1004\u103a\u101e\u100a\u103a &#8211; \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Binomial Distribution \u1014\u102d\u1012\u102b\u1014\u103a\u1038 - Statology<\/title>\n<meta name=\"description\" content=\"\u1010\u101b\u102c\u1038\u101d\u1004\u103a\u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1005\u103d\u102c \u1021\u1015\u102b\u1021\u101d\u1004\u103a binomial distribution \u1021\u1010\u103d\u1000\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u1014\u102d\u1012\u102b\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u104b\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/my\/binomial-\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1001\u103c\u1004\u103a\u1038\u104b\/\" \/>\n<meta property=\"og:locale\" content=\"my_MM\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binomial 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