離散確率変数の期待値と分散

確率変数$X$が次の確率分布に従うとき、期待値$E[X]$と分散$V[X]$を求めなさい。$X$: 1, 2, 3　確率: $0.2, 0.5, 0.3$

$E[X] = 2.1$、$V[X] = 0.49$

$E[X] = 1(0.2)+2(0.5)+3(0.3) = 2.1$。$E[X^2] = 1^2(0.2)+2^2(0.5)+3^2(0.3) = 0.2+2.0+2.7=4.9$。よって $V[X] = E[X^2]-(E[X])^2 = 4.9 - 2.1^2 = 4.9-4.41=0.49$。