关于随机变量的一些题麻烦各位大虾了.

1.
(1).
X B[8 ,1/4] ,
E(X) = 8 * 1/4 = 2 ,D(X) = 8 * 1/4 * (1 - 1/4) = 3/2 ,
(2).
E(Y) = E(6X) = 6 E(X) = 12 .
2.
(1).
1/6 + 1/3 + 1/6 + a = 1 ==> a = 1/3 .
E(X) = 1 * 1/6 + 2 * 1/3 + 3 * 1/6 + 4 * 1/3 = 8/3 .
(2).
E(N) = E(2X+3) = 2 E(X) + 3 = 25/3 .
3.
E(Y) = 0 + 1 * 0.2 + 2 * 0.4 + 3 * 0.1 + 4 * 0.2 = 2.1 ,
E(Y^2) = 0 + 1 * 0.2 + 4 * 0.4 + 9 * 0.1 + 16 * 0.2 = 5.9 ,
D(Y) = E(Y^2) - [E(Y)]^2 = 5.9 - 4.41 = 1.49 .
4.
(1).
E(X) = 0 + 1 * 1/2 + 2 * 1/6 = 5/6 ,
D(X) = (0 - 5/6)^2 * 1/3 + (1 - 5/6)^2 * 1/2 + (2 - 5/6)^2 * 1/6
= 17/36 ,
σ = √D(X) = √(17/36) = √17 / 6 .
(2).
E(N) = E(3X+1) = 3 E(X) + 1 = 7/2 ,
D(N) = D(3X+1) = 3^2 D(X) = 9 * 17/36 = 17/4 .