Let X and Y be be two independent random variables such that E(X) = E(Y) = 4 and Var(X) = Var(Y) = 2?

2016-12-01 3:35 pm
Define U = 3X − 2Y + 1 and V =
X(2Y + X). How to calculate E(U), E(V ) and Var(U)?

Thanks!

回答 (1)

2016-12-01 8:27 pm
✔ 最佳答案
E[U] = 3 E[X] - 2 E[Y] + 1 = 3 * 4 - 2 * 4 + 1 = 5.

E[V] = E[2XY + E[X^2]
........= 2 E[X] E[Y] + E[X^2], since X and Y are independent
........= 2 E[X] E[Y] + Var(X) + (E[X])^2
........= 2 * 4 * 4 + 2 + 4^2
........= 50.

Var(U) = Var(3X - 2Y + 1)
............= 3^2 Var(X) + (-2)^2 Var(Y) + 0, since X and Y are independent
............= 9 * 2 + 4 * 2
............= 26.

I hope this helps!


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