{"id":597,"date":"2023-07-29T09:18:19","date_gmt":"2023-07-29T09:18:19","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%a8%e0%a4%bf%e0%a4%b0%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%a4%e0%a4%be-%e0%a4%b8%e0%a5%81%e0%a4%a7%e0%a4%be%e0%a4%b0-%e0%a4%95%e0%a5%88%e0%a4%b2%e0%a4%95%e0%a5%81%e0%a4%b2%e0%a5%87%e0%a4%9f%e0%a4%b0\/"},"modified":"2023-07-29T09:18:19","modified_gmt":"2023-07-29T09:18:19","slug":"%e0%a4%a8%e0%a4%bf%e0%a4%b0%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%a4%e0%a4%be-%e0%a4%b8%e0%a5%81%e0%a4%a7%e0%a4%be%e0%a4%b0-%e0%a4%95%e0%a5%88%e0%a4%b2%e0%a4%95%e0%a5%81%e0%a4%b2%e0%a5%87%e0%a4%9f%e0%a4%b0","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%a8%e0%a4%bf%e0%a4%b0%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%a4%e0%a4%be-%e0%a4%b8%e0%a5%81%e0%a4%a7%e0%a4%be%e0%a4%b0-%e0%a4%95%e0%a5%88%e0%a4%b2%e0%a4%95%e0%a5%81%e0%a4%b2%e0%a5%87%e0%a4%9f%e0%a4%b0\/","title":{"rendered":"\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0941\u0927\u093e\u0930 \u0915\u0948\u0932\u0915\u0941\u0932\u0947\u091f\u0930"},"content":{"rendered":"<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>.axis--y .domain {\n  display: none;\n}<\/p>\n<p>h1 {\ntext-align: center;\nfont-size: 50px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>p {\ncolor: black;\ntext-align: center;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/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>#calcTitle {\ntext-align: center;\nfont-size: 20px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>#hr_top {\nwidth: 30%;\nmargin-bottom: 0px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#hr_bottom {\nwidth: 30%;\nmargin-top: 15px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>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    }\n#words_intro {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}\n<\/style>\n<div id=\"words_intro\"><b><a href=\"https:\/\/statorials.org\/hi\/\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e-\u0938\u0941\u0927\u093e\u0930\/\" target=\"_blank\" rel=\"noopener\">\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0941\u0927\u093e\u0930 \u0915\u093e<\/a><\/b> \u0909\u092a\u092f\u094b\u0917 \u0924\u092c \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0906\u092a \u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<\/div>\n<div id=\"words_intro\"> \u092f\u0939 \u0915\u0948\u0932\u0915\u0941\u0932\u0947\u091f\u0930 \u0906\u092a\u0915\u094b \u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u0905\u0928\u0941\u092e\u093e\u0928\u093f\u0924 \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u090f\u0902 \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u092e\u0947\u0902 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0941\u0927\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/div>\n<div id=\"words_intro\"> \u092c\u0938 \u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0917\u090f \u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u0909\u091a\u093f\u0924 \u092e\u093e\u0928 \u0926\u0930\u094d\u091c \u0915\u0930\u0947\u0902, \u092b\u093f\u0930 &#8220;\u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902&#8221; \u092c\u091f\u0928 \u092a\u0930 \u0915\u094d\u0932\u093f\u0915 \u0915\u0930\u0947\u0902\u0964<\/div>\n<div id=\"words\"> <label for=\"n\"><b>n<\/b> (\u092a\u0930\u0940\u0915\u094d\u0937\u0923\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e)<\/label><input type=\"number\" id=\"n\" min=\"0\" value=\"5\"><\/div>\n<div id=\"words\"> <label for=\"X\"><b>\u090f\u0915\u094d\u0938<\/b> (\u0938\u092b\u0932\u0924\u093e\u0913\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e)<\/label><input type=\"number\" id=\"X\" min=\"0\" value=\"3\"><\/div>\n<div id=\"words\"> <label for=\"p\"><b>\u092a\u0940<\/b> (\u0915\u093f\u0938\u0940 \u0926\u093f\u090f \u0917\u090f \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u092e\u0947\u0902 \u0938\u092b\u0932\u0924\u093e \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e)<\/label> <input type=\"number\" id=\"p\" min=\"0\" value=\"0.4\" step=\".01\"><\/div>\n<div id=\"words\"><input type=\"button\" id=\"button\" onclick=\"binomialCalc()\" value=\"Calculate\"><\/div>\n<div id=\"words\"> <b>\u0938\u091f\u0940\u0915 \u0926\u094d\u0935\u093f\u092a\u0926 \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u090f\u0901:<\/b><\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938 = <span class=\"user_X\">3<\/span> ): <span id=\"exactProb\">0.23040<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938 \u2264 <span class=\"user_X\">3<\/span> ): <span id=\"lessEqualProb\">0.92196<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938 &lt; <span class=\"user_X\">3<\/span> ): <span id=\"lessProb\">0.68256<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940( <span class=\"user_X\">\u090f\u0915\u094d\u0938\u22653<\/span> ): <span id=\"greaterEqualProb\">0.31744<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938 &gt; <span class=\"user_X\">3<\/span> ): <span id=\"greaterProb\">0.08704<\/span><\/p>\n<\/div>\n<div id=\"words\"> <b>\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0941\u0927\u093e\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0905\u0928\u0941\u092e\u093e\u0928\u093f\u0924 \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u090f\u0901:<\/b><\/div>\n<div>\n<p> \u092a\u0940( <span id=\"user_X1\">2.5<\/span> &lt;\u090f\u0915\u094d\u0938 &lt; <span id=\"user_X2\">3.5<\/span> ): <span id=\"approxProb1\">0.23040<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938&lt; <span id=\"user_X3\">3.5<\/span> ): <span id=\"approxProb2\">0.92196<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938 &lt; <span id=\"user_X4\">2.5<\/span> ): <span id=\"approxProb3\">0.68256<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938 &gt; <span id=\"user_X5\">2.5<\/span> ): <span id=\"approxProb4\">0.31744<\/span><\/p>\n<\/div>\n<div>\n<p> \u092a\u0940(\u090f\u0915\u094d\u0938 &gt; <span id=\"user_X6\">3.5<\/span> ): <span id=\"approxProb5\">0.08704<\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>function binomialCalc() {<\/p>\n<p>\/\/get input values\nvar X = document.getElementById('X').value;\nvar p = document.getElementById('p').value;\nvar n = document.getElementById('n').value;<\/p>\n<p>\/\/calculate cumulative probabilities\t\nvar probArray = [];\nfor (var i = 0; i <= X; i++) {\n\tprobArray[i] = (math.factorial(n) \/ (math.factorial(n-i) * math.factorial(i))) * Math.pow(p, i) * Math.pow((1-p), (n-i));\n\t}\n\n\/\/assign probabilities to variable names\nvar exactProb = (math.factorial(n) \/ (math.factorial(n-X) * math.factorial(X))) * Math.pow(p, X) * Math.pow((1-p), (n-X));\nvar lessEqualProb = math.sum(probArray);\nvar lessProb = lessEqualProb - exactProb;\nvar greaterEqualProb = 1 - lessProb;\nvar greaterProb = 1 - lessEqualProb;\n\n\/\/output probabilities\ndocument.getElementById('exactProb').innerHTML = exactProb.toFixed(5);\ndocument.getElementById('lessEqualProb').innerHTML = lessEqualProb.toFixed(5);\ndocument.getElementById('lessProb').innerHTML = lessProb.toFixed(5);\ndocument.getElementById('greaterEqualProb').innerHTML = greaterEqualProb.toFixed(5);\ndocument.getElementById('greaterProb').innerHTML = greaterProb.toFixed(5);\n\n\/\/change X to reflect value that user entered\ndocument.getElementsByClassName('user_X')[0].innerHTML = X;\ndocument.getElementsByClassName('user_X')[1].innerHTML = X;\ndocument.getElementsByClassName('user_X')[2].innerHTML = X;\ndocument.getElementsByClassName('user_X')[3].innerHTML = X;\ndocument.getElementsByClassName('user_X')[4].innerHTML = X;\n\n\/\/find correct continuity correction values\nvar user_X1 = X-.5;\nvar user_X2 = X-(-.5);\nvar user_X3 = X-(-.5);\nvar user_X4 = X-.5;\nvar user_X5 = X-.5;\nvar user_X6 = X-(-.5);\n\n\/\/apply continuity correction values\ndocument.getElementById('user_X1').innerHTML = (user_X1).toFixed(1);\ndocument.getElementById('user_X2').innerHTML = (user_X2).toFixed(1);\ndocument.getElementById('user_X3').innerHTML = (user_X3).toFixed(1);\ndocument.getElementById('user_X4').innerHTML = (user_X4).toFixed(1);\ndocument.getElementById('user_X5').innerHTML = (user_X5).toFixed(1);\ndocument.getElementById('user_X6').innerHTML = (user_X6).toFixed(1);\n\n\/\/find z scores\nvar mean_z = n*p;\nvar stdev_z = Math.sqrt(n*p*(1-p));\n\n\/\/find z-scores\nvar approxProb1 = jStat.normal.cdf(user_X2, mean_z, stdev_z) - jStat.normal.cdf(user_X1, mean_z, stdev_z);\nvar approxProb2 = jStat.normal.cdf(user_X3, mean_z, stdev_z);\nvar approxProb3 = jStat.normal.cdf(user_X4, mean_z, stdev_z);\nvar approxProb4 = 1-jStat.normal.cdf(user_X5, mean_z, stdev_z);\nvar approxProb5 = 1-jStat.normal.cdf(user_X6, mean_z, stdev_z);\n\n\/\/output probabilities\ndocument.getElementById('approxProb1').innerHTML = approxProb1.toFixed(5);\ndocument.getElementById('approxProb2').innerHTML = approxProb2.toFixed(5);\ndocument.getElementById('approxProb3').innerHTML = approxProb3.toFixed(5);\ndocument.getElementById('approxProb4').innerHTML = approxProb4.toFixed(5);\ndocument.getElementById('approxProb5').innerHTML = approxProb5.toFixed(5);\n}\n\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0941\u0927\u093e\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u092c \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0906\u092a \u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0915\u0948\u0932\u0915\u0941\u0932\u0947\u091f\u0930 \u0906\u092a\u0915\u094b \u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u0905\u0928\u0941\u092e\u093e\u0928\u093f\u0924 \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u090f\u0902 \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u092e\u0947\u0902 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0941\u0927\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u092c\u0938 \u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0917\u090f \u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f [&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":[],"class_list":["post-597","post","type-post","status-publish","format-standard","hentry","category-3"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0941\u0927\u093e\u0930 \u0915\u0948\u0932\u0915\u094d\u092f\u0942\u0932\u0947\u091f\u0930 - 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