﻿{"id":2969,"date":"2013-05-10T17:01:31","date_gmt":"2013-05-10T08:01:31","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=2969"},"modified":"2017-04-27T08:48:49","modified_gmt":"2017-04-26T23:48:49","slug":"%e7%a2%ba%e7%8e%87%e5%88%86%e5%b8%83%e3%81%94%e3%81%a8%e3%81%ae%e7%a2%ba%e7%8e%87%e5%af%86%e5%ba%a6%e9%96%a2%e6%95%b0%e3%81%8a%e3%82%88%e3%81%b3%e6%9c%9f%e5%be%85%e5%80%a4%e3%81%a8%e5%88%86%e6%95%a3-2","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=2969","title":{"rendered":"\u78ba\u7387\u5206\u5e03\u3054\u3068\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u304a\u3088\u3073\u671f\u5f85\u5024\u3068\u5206\u6563"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000\u78ba\u7387\u5206\u5e03\u3054\u3068\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570 f(x), \u78ba\u7387\u5909\u6570 X \u306e\u671f\u5f85\u5024 E(X) \u304a\u3088\u3073\u5206\u6563 V(X) \u3092\u307e\u3068\u3081\u307e\u3057\u305f\uff0e<\/p>\n<table border=\"0\" align=\"left\">\n<tbody>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u8d85\u5e7e\u4f55\u5206\u5e03<\/span><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7B%7B%7D_%7BM%7DC_x%5Ccdot%7B%7D_%7BN-M%7DC_%7Bn-x%7D%7D%7B%7B%7D_%7BN%7DC_%7Bn%7D%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{{}_{M}C_x\\cdot{}_{N-M}C_{n-x}}{{}_{N}C_{n}}' title='\\displaystyle f(x) = \\frac{{}_{M}C_x\\cdot{}_{N-M}C_{n-x}}{{}_{N}C_{n}}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3D+Max%280%2C+n+-+%28N+-+M%29%29%2C+%5Ccdots%2C+Min%28n%2C+M%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x = Max(0, n - (N - M)), \\cdots, Min(n, M)' title='\\displaystyle x = Max(0, n - (N - M)), \\cdots, Min(n, M)' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+E%28X%29+%3D+np&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle E(X) = np' title='\\displaystyle E(X) = np' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+p+%3D+%5Cfrac%7BM%7D%7BN%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle p = \\frac{M}{N}' title='\\displaystyle p = \\frac{M}{N}' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+np%281+-+p%29%5Cfrac%7BN+-+n%7D%7BN+-+1%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = np(1 - p)\\frac{N - n}{N - 1}' title='\\displaystyle V(X) = np(1 - p)\\frac{N - n}{N - 1}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u4e8c\u9805\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%7B%7D_%7Bn%7DC_%7Bx%7Dp%5E%7Bx%7D%281+-+p%29%5E%7Bn+-+x%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = {}_{n}C_{x}p^{x}(1 - p)^{n - x}' title='\\displaystyle f(x) = {}_{n}C_{x}p^{x}(1 - p)^{n - x}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3D+0%2C+1%2C+%5Ccdots%2C+n&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x = 0, 1, \\cdots, n' title='\\displaystyle x = 0, 1, \\cdots, n' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+E%28X%29+%3D+np&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle E(X) = np' title='\\displaystyle E(X) = np' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+0+%3C+p+%3C+1%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+V%28X%29+%3D+np%281+-+p%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle 0 &lt; p &lt; 1&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle V(X) = np(1 - p)' title='\\displaystyle 0 &lt; p &lt; 1&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle V(X) = np(1 - p)' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u30dd\u30a2\u30bd\u30f3\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7B%5Cexp%28-+%5Clambda%29%5Ccdot%5Clambda%5Ex%7D%7Bx%21%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{\\exp(- \\lambda)\\cdot\\lambda^x}{x!}' title='\\displaystyle f(x) = \\frac{\\exp(- \\lambda)\\cdot\\lambda^x}{x!}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3D+0%2C+1%2C+2%2C+%5Ccdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x = 0, 1, 2, \\cdots' title='\\displaystyle x = 0, 1, 2, \\cdots' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+E%28X%29+%3D+%5Clambda&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle E(X) = \\lambda' title='\\displaystyle E(X) = \\lambda' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clambda+%3D+np&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\lambda = np' title='\\lambda = np' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Clambda&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\lambda' title='\\displaystyle V(X) = \\lambda' class='latex' \/><\/td>\n<td><\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u5e7e\u4f55\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+p%281+-+p%29%5E%7Bx+-+1%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = p(1 - p)^{x - 1}' title='\\displaystyle f(x) = p(1 - p)^{x - 1}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3D+1%2C+2%2C+3%2C+%5Ccdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x = 1, 2, 3, \\cdots' title='\\displaystyle x = 1, 2, 3, \\cdots' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+E%28X%29+%3D+%5Cfrac%7B1%7D%7Bp%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle E(X) = \\frac{1}{p}' title='\\displaystyle E(X) = \\frac{1}{p}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+0+%3C+p+%3C+1%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+V%28X%29+%3D+%5Cfrac%7B1+-+p%7D%7Bp%5E2%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle 0 &lt; p &lt; 1&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle V(X) = \\frac{1 - p}{p^2}' title='\\displaystyle 0 &lt; p &lt; 1&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle V(X) = \\frac{1 - p}{p^2}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u8ca0\u306e\u4e8c\u9805\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%7B%7D_%7Bk+%2B+x+-+1%7DC_%7Bx%7Dp%5E%7Bk%7D%281-p%29%5E%7Bx%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = {}_{k + x - 1}C_{x}p^{k}(1-p)^{x}' title='\\displaystyle f(x) = {}_{k + x - 1}C_{x}p^{k}(1-p)^{x}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3D+0%2C+1%2C+2%2C+%5Ccdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x = 0, 1, 2, \\cdots' title='\\displaystyle x = 0, 1, 2, \\cdots' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+E%28X%29+%3D+%5Cfrac%7Bk%281+-+p%29%7D%7Bp%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle E(X) = \\frac{k(1 - p)}{p}' title='\\displaystyle E(X) = \\frac{k(1 - p)}{p}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Cfrac%7Bk%281+-+p%29%7D%7Bp%5E2%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\frac{k(1 - p)}{p^2}' title='\\displaystyle V(X) = \\frac{k(1 - p)}{p^2}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u6b63\u898f\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7B1%7D%7B%5Csqrt%7B2%5Cpi%7D%5Csigma%7D%5Cexp%5Cleft%28-%5Cfrac%7B%28x+-+m%29%5E2%7D%7B2%5Csigma%5E2%7D%5Cright%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma}\\exp\\left(-\\frac{(x - m)^2}{2\\sigma^2}\\right)' title='\\displaystyle f(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma}\\exp\\left(-\\frac{(x - m)^2}{2\\sigma^2}\\right)' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+-+%5Cinfty+%3C+x+%3C+%5Cinfty%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+E%28X%29+%3D+m&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle - \\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = m' title='\\displaystyle - \\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = m' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Csigma%5E2&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\sigma^2' title='\\displaystyle V(X) = \\sigma^2' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Csigma+%3E+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\sigma &gt; 0' title='\\displaystyle \\sigma &gt; 0' class='latex' \/><\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u6307\u6570\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Clambda%5Cexp%28-%5Clambda+x%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\lambda\\exp(-\\lambda x)' title='\\displaystyle f(x) = \\lambda\\exp(-\\lambda x)' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%5Cge+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x \\ge 0' title='\\displaystyle x \\ge 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = 0' title='\\displaystyle f(x) = 0' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3C+0%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+E%28X%29+%3D+%5Cfrac%7B1%7D%7B%5Clambda%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\frac{1}{\\lambda}' title='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\frac{1}{\\lambda}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Cfrac%7B1%7D%7B%5Clambda%5E2%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\frac{1}{\\lambda^2}' title='\\displaystyle V(X) = \\frac{1}{\\lambda^2}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u30ac\u30f3\u30de\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7B%5Clambda%5E%5Calpha%7D%7B%5CGamma%28%5Calpha%29%7Dx%5E%7B%5Calpha+-+1%7D%5Cexp%28-+%5Clambda+x%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{\\lambda^\\alpha}{\\Gamma(\\alpha)}x^{\\alpha - 1}\\exp(- \\lambda x)' title='\\displaystyle f(x) = \\frac{\\lambda^\\alpha}{\\Gamma(\\alpha)}x^{\\alpha - 1}\\exp(- \\lambda x)' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%5Cge+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x \\ge 0' title='\\displaystyle x \\ge 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = 0' title='\\displaystyle f(x) = 0' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3C+0%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+E%28X%29+%3D+%5Cfrac%7B%5Calpha%7D%7B%5Clambda%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\frac{\\alpha}{\\lambda}' title='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\frac{\\alpha}{\\lambda}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Clambda%2C+%5Calpha+%3E+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\lambda, \\alpha &gt; 0' title='\\displaystyle \\lambda, \\alpha &gt; 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Cfrac%7B%5Calpha%7D%7B%5Clambda%5E2%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\frac{\\alpha}{\\lambda^2}' title='\\displaystyle V(X) = \\frac{\\alpha}{\\lambda^2}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u30d9\u30fc\u30bf\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7Bx%5E%7B%5Calpha+-+1%7D%281+-+x%29%5E%7B%5Cbeta+-+1%7D%7D%7BB%28%5Calpha%2C+%5Cbeta%29%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{x^{\\alpha - 1}(1 - x)^{\\beta - 1}}{B(\\alpha, \\beta)}' title='\\displaystyle f(x) = \\frac{x^{\\alpha - 1}(1 - x)^{\\beta - 1}}{B(\\alpha, \\beta)}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+0+%3C+x+%3C+1%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+f%28x%29+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle 0 &lt; x &lt; 1&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle f(x) = 0' title='\\displaystyle 0 &lt; x &lt; 1&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle f(x) = 0' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%5Cle+0%2C+1+%5Cle+x&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x \\le 0, 1 \\le x' title='\\displaystyle x \\le 0, 1 \\le x' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+E%28X%29+%3D+%5Cfrac%7B%5Calpha%7D%7B%5Calpha+%2B+%5Cbeta%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle E(X) = \\frac{\\alpha}{\\alpha + \\beta}' title='\\displaystyle E(X) = \\frac{\\alpha}{\\alpha + \\beta}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Cfrac%7B%5Calpha%5Cbeta%7D%7B%28%5Calpha+%2B+%5Cbeta%29%5E2%28%5Calpha+%2B+%5Cbeta+%2B+1%29%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\frac{\\alpha\\beta}{(\\alpha + \\beta)^2(\\alpha + \\beta + 1)}' title='\\displaystyle V(X) = \\frac{\\alpha\\beta}{(\\alpha + \\beta)^2(\\alpha + \\beta + 1)}' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u30b3\u30fc\u30b7\u30fc\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7B%5Calpha%7D%7B%5Cpi%28%5Calpha%5E2+%2B+%28x+-+%5Clambda%29%5E2%29%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{\\alpha}{\\pi(\\alpha^2 + (x - \\lambda)^2)}' title='\\displaystyle f(x) = \\frac{\\alpha}{\\pi(\\alpha^2 + (x - \\lambda)^2)}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Calpha+%3E+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\alpha &gt; 0' title='\\displaystyle \\alpha &gt; 0' class='latex' \/><\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u5bfe\u6570\u6b63\u898f\u5206\u5e03<\/span><\/td>\n<td><span style=\"color: #ffffff;\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7B1%7D%7B%5Csqrt%7B2%5Cpi%7D%5Csigma+x%7D%5Cexp%5Cleft%28-%5Cfrac%7B%28%5Clog%28x%29+-+m%29%5E2%7D%7B2%5Csigma%5E2%7D%5Cright%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma x}\\exp\\left(-\\frac{(\\log(x) - m)^2}{2\\sigma^2}\\right)' title='\\displaystyle f(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma x}\\exp\\left(-\\frac{(\\log(x) - m)^2}{2\\sigma^2}\\right)' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3E+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x &gt; 0' title='\\displaystyle x &gt; 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = 0' title='\\displaystyle f(x) = 0' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%5Cle+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x \\le 0' title='\\displaystyle x \\le 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+E%28X%29+%3D+%5Cexp%5Cleft%28m+%2B+%5Cfrac%7B%5Csigma%5E2%7D%7B2%7D%5Cright%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle E(X) = \\exp\\left(m + \\frac{\\sigma^2}{2}\\right)' title='\\displaystyle E(X) = \\exp\\left(m + \\frac{\\sigma^2}{2}\\right)' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Csigma+%3E+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\sigma &gt; 0' title='\\displaystyle \\sigma &gt; 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Cexp%5B2m+%2B+%5Csigma%5E2%5D%28%5Cexp%5B%5Csigma%5E2%5D+-+1%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\exp[2m + \\sigma^2](\\exp[\\sigma^2] - 1)' title='\\displaystyle V(X) = \\exp[2m + \\sigma^2](\\exp[\\sigma^2] - 1)' class='latex' \/><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u30d1\u30ec\u30fc\u30c8\u5206\u5e03<\/span><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7Bx_0%5E%5Calpha%7D%7Bx%5E%7B%5Calpha+%2B+1%7D%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{x_0^\\alpha}{x^{\\alpha + 1}}' title='\\displaystyle f(x) = \\frac{x_0^\\alpha}{x^{\\alpha + 1}}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%5Cge+x_0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x \\ge x_0' title='\\displaystyle x \\ge x_0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = 0' title='\\displaystyle f(x) = 0' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3C+0%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+E%28X%29+%3D+%5Cfrac%7Bax_0%7D%7Ba+-+1%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\frac{ax_0}{a - 1}' title='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\frac{ax_0}{a - 1}' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+a+%3E+1&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle a &gt; 1' title='\\displaystyle a &gt; 1' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Cfrac%7Bax_0%5E2%7D%7Ba+-+2%7D+-+%5Cleft%28%5Cfrac%7Bax_0%7D%7Ba+-+1%7D%5Cright%29%5E2&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\frac{ax_0^2}{a - 2} - \\left(\\frac{ax_0}{a - 1}\\right)^2' title='\\displaystyle V(X) = \\frac{ax_0^2}{a - 2} - \\left(\\frac{ax_0}{a - 1}\\right)^2' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+a+%3E+2&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle a &gt; 2' title='\\displaystyle a &gt; 2' class='latex' \/><\/td>\n<\/tr>\n<tr style=\"background-color: #a9a9a9;\">\n<td><span style=\"color: #ffffff;\">\u30ef\u30a4\u30d6\u30eb\u5206\u5e03<\/span><\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+%5Cfrac%7B%5Cgamma+x%5E%7B%5Cgamma+-+1%7D%7D%7B%5Clambda%5Eb%7D%5Cexp%5Cleft%5B-%5Cleft%28%5Cfrac%7Bx%7D%7By%7D%5Cright%29%5E%5Cgamma%5Cright%5D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = \\frac{\\gamma x^{\\gamma - 1}}{\\lambda^b}\\exp\\left[-\\left(\\frac{x}{y}\\right)^\\gamma\\right]' title='\\displaystyle f(x) = \\frac{\\gamma x^{\\gamma - 1}}{\\lambda^b}\\exp\\left[-\\left(\\frac{x}{y}\\right)^\\gamma\\right]' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%5Cge+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x \\ge 0' title='\\displaystyle x \\ge 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = 0' title='\\displaystyle f(x) = 0' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+x+%3C+0%26%2391%3B%2Flatex%26%2393%3B%3C%2Ftd%3E++%3C%2Ftr%3E++%3Ctr%3E++%3Ctd%3E%5Blatex%5D%5Cdisplaystyle+E%28X%29+%3D+%5Clambda%5CGamma%5Cleft%281+%2B+%5Cfrac%7B1%7D%7B%5Cgamma%7D%5Cright%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\lambda\\Gamma\\left(1 + \\frac{1}{\\gamma}\\right)' title='\\displaystyle x &lt; 0&#091;\/latex&#093;&lt;\/td&gt;  &lt;\/tr&gt;  &lt;tr&gt;  &lt;td&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle E(X) = \\lambda\\Gamma\\left(1 + \\frac{1}{\\gamma}\\right)' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Clambda+%3E+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\lambda &gt; 0' title='\\displaystyle \\lambda &gt; 0' class='latex' \/><\/td>\n<\/tr>\n<tr>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+V%28X%29+%3D+%5Clambda%5E2%5Cleft%5B%5CGamma%5Cleft%282+%2B+%5Cfrac%7B1%7D%7B%5Cgamma%7D%5Cright%29+-+%5Cleft%28%5CGamma%5Cleft%281+%2B+%5Cfrac%7B1%7D%7B%5Cgamma%7D%5Cright%29%5Cright%29%5E2%5Cright%5D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle V(X) = \\lambda^2\\left[\\Gamma\\left(2 + \\frac{1}{\\gamma}\\right) - \\left(\\Gamma\\left(1 + \\frac{1}{\\gamma}\\right)\\right)^2\\right]' title='\\displaystyle V(X) = \\lambda^2\\left[\\Gamma\\left(2 + \\frac{1}{\\gamma}\\right) - \\left(\\Gamma\\left(1 + \\frac{1}{\\gamma}\\right)\\right)^2\\right]' class='latex' \/><\/td>\n<td><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cgamma+%3E+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\gamma &gt; 0' title='\\displaystyle \\gamma &gt; 0' class='latex' \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><iframe loading=\"lazy\" width=\"320\" height=\"240\" style=\"width: 120px; height: 240px;\" src=\"\/\/rcm-jp.amazon.co.jp\/e\/cm?lt1=_blank&amp;bc1=000000&amp;IS2=1&amp;bg1=FFFFFF&amp;fc1=000000&amp;lc1=0000FF&amp;t=fujiitoshiki-22&amp;o=9&amp;p=8&amp;l=as4&amp;m=amazon&amp;f=ifr&amp;ref=ss_til&amp;asins=4489020236\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u78ba\u7387\u5206\u5e03\u3054\u3068\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570 f(x), \u78ba\u7387\u5909\u6570 X \u306e\u671f\u5f85\u5024 E(X) \u304a\u3088\u3073\u5206\u6563 V(X) \u3092\u307e\u3068\u3081\u307e\u3057\u305f\uff0e \u8d85\u5e7e\u4f55\u5206\u5e03 \u00a0 \u00a0 \u4e8c\u9805\u5206\u5e03 \u00a0 \u00a0 \u30dd\u30a2\u30bd\u30f3\u5206\u5e03 \u00a0 \u5e7e\u4f55\u5206\u5e03 \u00a0 \u00a0 \u8ca0\u306e\u4e8c\u9805\u5206\u5e03 \u00a0 \u00a0 \u00a0 \u6b63\u898f &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=2969\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u78ba\u7387\u5206\u5e03\u3054\u3068\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u304a\u3088\u3073\u671f\u5f85\u5024\u3068\u5206\u6563&#8221; 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