{"blog_url":"https://randommemory.hatenablog.com/","author_url":"https://blog.hatena.ne.jp/derwind/","description":"\u6b21\u306b\u78ba\u7387\u5909\u6570\u306e\u548c\u306b\u95a2\u9023\u3057\u3066\u5206\u5e03\u306e\u518d\u751f\u6027\u306b\u3064\u3044\u3066\u6271\u3046\u3002[3] p.73 \u306e\u547d\u984c 4.20 \u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3002 $X,Y$ \u3092\u72ec\u7acb\u306a\u78ba\u7387\u5909\u6570\u3068\u3059\u308b\u6642 $Z = X+Y$ \u3068\u304a\u304f\u3068 \\begin{align} E[\\exp(it Z)] = E[\\exp(it (X+Y))] = E[\\exp(it X)] E[\\exp(it Y)] \\end{align}\u3068\u306a\u308b\u306e\u3067\u3001$Z$ \u306e\u7279\u6027\u51fd\u6570\u3092\u6c42\u3081\u3001\u518d\u3073L\u00e9vy \u306e\u53cd\u8ee2\u516c\u5f0f\u304b\u3089 $Z$ \u304c\u5f93\u3046\u78ba\u7387\u5206\u5e03\u3092\u6c42\u3081\u308b\u3002\u3053\u3053\u3067\u306f t \u5206\u5e03\u306e\u307f\u306b\u95a2\u5fc3\u304c\u3042\u308b\u305f\u3081\u6b63\u898f\u5206\u5e03\u3068\u30ab\u30a4 2 \u4e57\u5206\u5e03\u306e\u5834\u5408\u306e\u307f\u6271\u3046\u3002\u25cf\u6b63\u898f\u5206\u5e03\u306e\u5834\u5408 $X \\sim N(\\mu_1,\\sigma\u2026","version":"1.0","image_url":null,"provider_name":"Hatena Blog","author_name":"derwind","published":"2020-07-29 21:59:26","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2020%2F07%2F29%2F215926\" title=\"t\u5206\u5e03\u3078\u306e\u9053 (5) - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","categories":["statistics","math-probability"],"height":"190","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","url":"https://randommemory.hatenablog.com/entry/2020/07/29/215926","title":"t\u5206\u5e03\u3078\u306e\u9053 (5)","width":"100%","type":"rich","provider_url":"https://hatena.blog"}