{"id":767,"date":"2023-07-28T20:00:37","date_gmt":"2023-07-28T20:00:37","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%99%e1%80%8a%e1%80%ba%e1%80%99%e1%80%bb%e1%80%ad%e1%80%af%e1%80%b8%e1%80%85%e1%80%af%e1%80%b6-%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%b8-2\/"},"modified":"2023-07-28T20:00:37","modified_gmt":"2023-07-28T20:00:37","slug":"%e1%80%a1%e1%80%99%e1%80%8a%e1%80%ba%e1%80%99%e1%80%bb%e1%80%ad%e1%80%af%e1%80%b8%e1%80%85%e1%80%af%e1%80%b6-%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%b8-2","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%99%e1%80%8a%e1%80%ba%e1%80%99%e1%80%bb%e1%80%ad%e1%80%af%e1%80%b8%e1%80%85%e1%80%af%e1%80%b6-%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%b8-2\/","title":{"rendered":"Multinomial distribution \u1014\u102d\u1012\u102b\u1014\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u101b\u101c\u1012\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u101e\u100a\u103a \u1015\u102f\u1036\u101e\u1031<\/strong> \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101b\u103e\u102d\u101e\u100a\u1037\u103a <em>k<\/em> \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1010\u102d\u1000\u103b\u101e\u1031\u102c\u101b\u1031\u1010\u103d\u1000\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1010\u1005\u103a\u1001\u102f\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<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>\u1000\u103b\u1015\u1014\u103a\u1038<\/sub> <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=\"noopener\">variable<\/a> <sub>_<\/sub> <em>\u1000\u102d\u102f<\/em> \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 <sub>\u101c\u103b\u103e\u1004\u103a<\/sub> &#8211;<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 =<\/strong> <strong>n * (p <sub>1<\/sub> <sup>x <sub>1<\/sub><\/sup> * p <sub>2<\/sub> <sup>x <sub>2<\/sub><\/sup> * \u2026 * p <sub>k<\/sub> <sup>x <sub>k<\/sub><\/sup> ) \/ (x <sub>1<\/sub> ! * x <sub>2<\/sub> ! \u2026 * x <sub>k<\/sub> !)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n-<\/strong> \u1016\u103c\u1005\u103a\u101b\u1015\u103a\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>1<\/sub> :<\/strong> \u101b\u101c\u1012\u103a 1 \u1016\u103c\u1005\u103a\u1015\u1031\u102b\u103a\u101e\u100a\u1037\u103a \u1021\u1000\u103c\u102d\u1019\u103a\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>1<\/sub> :<\/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 \u101b\u101c\u1012\u103a 1 \u101e\u100a\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1021\u102d\u102f\u1038\u1011\u1032\u1010\u103d\u1004\u103a \u1021\u1014\u102e\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1045 \u101c\u102f\u1036\u1038\u104a \u1021\u1005\u102d\u1019\u103a\u1038\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1043 \u101c\u102f\u1036\u1038\u1014\u103e\u1004\u1037\u103a \u1021\u1015\u103c\u102c\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1042 \u101c\u102f\u1036\u1038 \u101b\u103e\u102d\u101e\u100a\u103a \u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1002\u1030\u1011\u1032\u1019\u103e \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1045 \u1001\u102f\u1000\u102d\u102f \u1000\u103b\u1015\u1014\u103a\u1038\u1006\u103d\u1032\u1011\u102f\u1010\u103a\u1015\u103c\u102e\u1038 \u1021\u1005\u102c\u1038\u1011\u102d\u102f\u1038\u1015\u102b\u1000\u104a \u1021\u1014\u102e\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1042 \u101c\u102f\u1036\u1038\u104a \u1021\u1005\u102d\u1019\u103a\u1038\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1042 \u101c\u102f\u1036\u1038 \u1014\u103e\u1004\u1037\u103a \u1021\u1015\u103c\u102c\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1041 \u101c\u102f\u1036\u1038 \u101b\u101b\u103e\u102d\u101b\u1014\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<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038\u1000\u102d\u102f\u1016\u103c\u1031\u1006\u102d\u102f\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1000\u1014\u1037\u103a\u101e\u1010\u103a\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u1019\u103b\u102d\u102f\u1038\u1019\u103b\u102d\u102f\u1038\u101e\u1031\u102c \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : \u1045<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>1<\/sub><\/strong> (# \u1021\u1014\u102e\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a\u1019\u103b\u102c\u1038) = 2\u104a<\/span> <span style=\"color: #000000;\"><strong>x <sub>2<\/sub><\/strong> (# \u1021\u1005\u102d\u1019\u103a\u1038\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a\u1019\u103b\u102c\u1038) = 2\u104a<\/span> <span style=\"color: #000000;\"><strong>x <sub>3<\/sub><\/strong> (# \u1021\u1015\u103c\u102c\u101b\u1031\u102c\u1004\u103a \u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a\u1019\u103b\u102c\u1038) = 1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>1<\/sub><\/strong> (\u1021\u1014\u102e\u101b\u1031\u102c\u1004\u103a prob.) = 0.5\u104a<\/span> <span style=\"color: #000000;\"><strong>p <sub>2<\/sub><\/strong> (\u1021\u1005\u102d\u1019\u103a\u1038\u101b\u1031\u102c\u1004\u103a prob.) = 0.3\u104a<\/span> <span style=\"color: #000000;\"><strong>p <sub>3<\/sub><\/strong> (\u1021\u1015\u103c\u102c\u101b\u1031\u102c\u1004\u103a prob.) = 0.2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1024\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1011\u1032\u101e\u102d\u102f\u1037 \u1015\u1031\u102b\u1004\u103a\u1038\u1011\u100a\u1037\u103a\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031<\/strong> = 5 * (.5 <sup>2<\/sup> * .3 <sup>2<\/sup> * .2 <sup>1<\/sup> ) \/ (2! * 2! * 1!) = <strong>0.135<\/strong> \u104b<\/span><\/p>\n<h2> <strong>Multinomial Distribution Practice \u1015\u103c\u103f\u1014\u102c\u1019\u103b\u102c\u1038<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1019\u100a\u103a\u1015\u1031\u102b\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1005\u103d\u102c \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<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a-<\/strong> \u1024\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u1016\u103c\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a <a href=\"https:\/\/statorials.org\/my\/multinomial-\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">Multinomial Distribution Calculator \u1000\u102d\u102f<\/a> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/em><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1015\u103c\u103f\u1014\u102c \u1041<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> \u1019\u103c\u102d\u102f\u1037\u1010\u1031\u102c\u103a\u101d\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u101e\u102f\u1036\u1038\u1019\u103b\u102d\u102f\u1038 \u101b\u103d\u1031\u1038\u1000\u1031\u102c\u1000\u103a\u1015\u103d\u1032\u1010\u103d\u1004\u103a \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u101c\u103e\u101a\u103a\u101c\u1031\u102c\u1004\u103a\u1038 A \u1000 \u1006\u1014\u1039\u1012\u1019\u1032 \u1041\u1040 \u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u104a \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u101c\u103e\u101a\u103a\u101c\u1031\u102c\u1004\u103a\u1038 B \u1000 \u1006\u1014\u1039\u1012\u1019\u1032 \u1044\u1040 \u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038 \u101b\u101b\u103e\u102d\u1015\u103c\u102e\u1038 \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u101c\u103e\u101a\u103a C \u1000 \u1019\u1032 \u1045\u1040 \u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038 \u101b\u101b\u103e\u102d\u101e\u100a\u103a\u104b \u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1019\u1032\u1006\u1014\u1039\u1012\u101b\u103e\u1004\u103a \u1041\u1040 \u1026\u1038\u104f \u1000\u103b\u1015\u1014\u103a\u1038\u1014\u1019\u1030\u1014\u102c\u1000\u102d\u102f \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1015\u102b\u1000\u104a \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u101c\u103e\u101a\u103a\u101c\u1031\u102c\u1004\u103a\u1038 A \u1000\u102d\u102f \u1042 \u1026\u1038\u1000 \u1019\u1032\u1015\u1031\u1038\u1001\u1032\u1037\u1015\u103c\u102e\u1038 \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u101c\u103e\u101a\u103a\u101c\u1031\u102c\u1004\u103a\u1038 B \u1021\u1010\u103d\u1000\u103a \u1044 \u1026\u1038\u1000 \u1019\u1032\u1015\u1031\u1038\u1001\u1032\u1037\u1015\u103c\u102e\u1038 \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u101c\u103e\u101a\u103a\u101c\u1031\u102c\u1004\u103a\u1038 C \u1021\u1010\u103d\u1000\u103a \u1044 \u1026\u1038\u1000 \u1019\u1032\u1015\u1031\u1038\u1001\u1032\u1037\u1001\u103c\u1004\u103a\u1038 \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<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>\u1021\u1016\u103c\u1031-<\/strong> \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a Multinomial Distribution Calculator \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c <strong>0.0504 \u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \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<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8244 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc1.png\" alt=\"Multinomial Calculator \u1025\u1015\u1019\u102c\" width=\"260\" height=\"553\" srcset=\"\" sizes=\"\"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1015\u103c\u103f\u1014\u102c \u1042<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> \u1000\u103c\u103d\u1000\u103a\u1010\u103d\u1004\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1021\u101d\u102b\u101b\u1031\u102c\u1004\u103a\u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1046 \u101c\u102f\u1036\u1038\u104a \u1021\u1014\u102e\u101b\u1031\u102c\u1004\u103a\u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1042 \u101c\u102f\u1036\u1038\u1014\u103e\u1004\u1037\u103a \u1015\u1014\u103a\u1038\u101b\u1031\u102c\u1004\u103a\u1005\u1000\u103b\u1004\u103a\u1000\u103b\u1031\u102c\u1000\u103a \u1042 \u101c\u102f\u1036\u1038\u1015\u102b\u101b\u103e\u102d\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u102d\u102f\u1038\u1011\u1032\u1019\u103e \u1018\u1031\u102c\u101c\u102f\u1036\u1038 \u1044 \u101c\u102f\u1036\u1038\u1000\u102d\u102f \u1000\u103b\u1015\u1014\u103a\u1038 \u1021\u1005\u102c\u1038\u1011\u102d\u102f\u1038\u104d \u1021\u1005\u102c\u1038\u1011\u102d\u102f\u1038\u1015\u102b\u1000\u104a \u1018\u1031\u102c\u101c\u102f\u1036\u1038 \u1044 \u101c\u102f\u1036\u1038\u1005\u101c\u102f\u1036\u1038 \u1021\u101d\u102b\u101b\u1031\u102c\u1004\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<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>\u1021\u1016\u103c\u1031-<\/strong> \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a Multinomial Distribution Calculator \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c <strong>0.1296 \u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \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<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8246 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc2.png\" alt=\"Multinomial Probability Distribution \u1025\u1015\u1019\u102c\" width=\"261\" height=\"561\" srcset=\"\" sizes=\"\"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1015\u103c\u103f\u1014\u102c \u1043<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038-<\/strong> \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1014\u103e\u1005\u103a\u101a\u1031\u102c\u1000\u103a \u1010\u1005\u103a\u101a\u1031\u102c\u1000\u103a\u1000\u102d\u102f\u1010\u1005\u103a\u101a\u1031\u102c\u1000\u103a \u1005\u1005\u103a\u1010\u102f\u101b\u1004\u103a\u1000\u1005\u102c\u1038\u1014\u1031\u1010\u101a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1002\u102d\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 A \u1014\u102d\u102f\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c 0.5 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 B \u1000 \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1002\u102d\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f \u1021\u1014\u102d\u102f\u1004\u103a\u101b\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c 0.3 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1002\u102d\u1019\u103a\u1038\u1010\u103d\u1004\u103a \u101e\u101b\u1031\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u103e\u102c 0\u104a 2 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1021\u1000\u101a\u103a\u104d \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1002\u102d\u1019\u103a\u1038 10 \u1001\u102f \u1000\u1005\u102c\u1038\u1015\u102b\u1000 \u1021\u1018\u101a\u103a\u1014\u100a\u103a\u1038\u104b \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038 A \u1000 4 \u1000\u103c\u102d\u1019\u103a \u104a \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038 B \u1000 5 \u1000\u103c\u102d\u1019\u103a \u104a \u101e\u1030\u1010\u102d\u102f\u1037 1 \u1000\u103c\u102d\u1019\u103a \u101e\u101b\u1031\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 ?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>\u1021\u1016\u103c\u1031-<\/strong> \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a Multinomial Distribution Calculator \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a <strong>0.038272 \u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \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<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8247 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc3.png\" alt=\"Multinomial Distribution \u1025\u1015\u1019\u102c\" width=\"259\" height=\"544\" srcset=\"\" sizes=\"\"><\/p>\n<h3 data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><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><\/span><\/h3>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1018\u102f\u1036\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u102d\u1012\u102b\u1014\u103a\u1038\u1015\u1031\u1038\u101e\u100a\u103a-<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <a href=\"https:\/\/statorials.org\/my\/\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u101e\u102c\u1019\u102c\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1019\u102d\u1010\u103a\u1006\u1000\u103a<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/binomial-\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f-\u1041\/\" target=\"_blank\" rel=\"noopener\">binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1001\u103c\u1004\u103a\u1038\u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1014\u102d\u1012\u102b\u1014\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/\u1004\u102b\u1038\u1016\u103c\u1014\u1037\u103a\u1001\u103b\u102e\u101b\u1031\u1038\/\" target=\"_blank\" rel=\"noopener\">Poisson \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1019\u102d\u1010\u103a\u1006\u1000\u103a<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/\u1002\u103b\u102e\u1029\u1019\u1031\u1010\u103c\u102e-\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1001\u103c\u1004\u103a\u1038\u104b\/\" target=\"_blank\" rel=\"noopener\">\u1002\u103b\u102e\u1029\u1019\u1031\u1010\u103c\u102e \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f \u1019\u102d\u1010\u103a\u1006\u1000\u103a<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u101b\u101c\u1012\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u101e\u100a\u103a \u1015\u102f\u1036\u101e\u1031 \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101b\u103e\u102d\u101e\u100a\u1037\u103a k \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1010\u102d\u1000\u103b\u101e\u1031\u102c\u101b\u1031\u1010\u103d\u1000\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1010\u1005\u103a\u1001\u102f\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 \u1000\u103b\u1015\u1014\u103a\u1038 variable _ \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 \u101c\u103b\u103e\u1004\u103a &#8211; \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 = n * (p 1 x 1 * p 2 x 2 * \u2026 * p k x k ) \/ (x 1 ! * x 2 ! \u2026 * x k !) \u101b\u103d\u103e\u1031- n- \u1016\u103c\u1005\u103a\u101b\u1015\u103a\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038 x 1 [&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>Multinomial Distribution - Statology \u1014\u102d\u1012\u102b\u1014\u103a\u1038<\/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 \u1021\u1019\u100a\u103a\u1019\u103b\u102d\u102f\u1038\u1005\u102f\u1036 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a 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