수리통계학

Chap1. Probability and Distributions Introduction Statistical experiment: Outcome that cannot be predicted with certainty prior to the experiment 통

$0\\le P(C)\\le1, \\ \\forall c \\in B$$0=P(\\phi) \\le P(c) \\le P(C) = 1$$P(C_1 \\cup C_2) = P(C_1) + P(C_2) - P(C_1 \\cap C_2)$$P(C_1 \\cup C_2) =

Random Variables(확률변수) -> 특정 확률분포를 따르는 변수(임의변수)$X: a\\ real\\ valued\\ function\\ defined\\ on\\ the\\ sample\\ space$$X(c) = k,\\ c \\in C$\--> one a

$X$: 셀수 있고 유한한 표본 공간 내의 확률변수discrete r.v. if ists space is either finite or countable$P_x(X) = P(X=x), x \\in S$지지영역(Support): $S_x =${$X:P_x(x) >0$}e

1.9 Some Special Expectation $E(X^k)$: k-th moment $\mu = E(X): mean$ $\sigma^2 := E{(X-\mu)^2}: variance$ $E{(X-\mu)^k}$: k-th central moment Def 1.

$k \\le m, \\ \\ \\E\\left| x \\right|^m < \\infin \\to E\\left| x \\right|^k < \\infin$$\\mu(X)$: 음수가 아닌 확률변수 X의 함수$E\\mu(x) < \\infin$=> $\

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