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# let X,Y,Z be three independent N(0,1) random variables a) Let W = X +2Y +3Z, what are the mean, variance, skewness, excess kurtosis of W?

let X,Y,Z be three independent N(0,1) random variables

a) Let W = X +2Y +3Z, what are the mean, variance, skewness, excess kurtosis of W?

b) Let V= （X^2 ）+ Y*Z， what is the conditional distribution of V given X and Z?

c) What is the conditional distribution of V given X =1 and Z=2?

d) What is the conditional variance of V given Y and Z?

Great question... View the full answer

, (0,1) . = + 2 + 3 3 ℎℎ , , () = () + 2() + 3() = 0
() = () + 22 () + 32 () = 1 + 4 + 9 = 14 (0,14)ℎ 0 , = 2 + = = , = 2 + ℎ ℎ . ℎ , ℎ .
() = 2 () = 0 () = 2 () = 2
ℎ , ℎ 2 2 = =...

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