设随机变量 X X X只取有限个可能值 a i ( i = 0 , 1 , . . . , m ) a_i (i=0, 1, ..., m) ai(i=0,1,...,m),其概率分布为 P ( X = a i ) = p i P (X = a_i) = p_i P(X=ai)=pi. 则 X X X的数学期望,记为 E ( X ) E(X) E(X)或 E X EX EX,定义为:
E ( X ) = ∑ i a i p i E(X) = \sum\limits_ia_ip_i E(X)=i∑aipi<