Hi Im having a tough time with this question and cannot get

Hi, I\'m having a tough time with this question and cannot get my head around it. Let X and Y be independently standard normal random variables and let Z = X^2 + Y. If E[X]=E[X^3] = 0 and E[X^2] = 1 (as X~N(0,1)) Solve for E[Z], E[Z|X] and E[ZX]

Could someone explain to me the working out through this? Thanks.

$Hi, I\'m having a tough time with this question and cannot get my head around it. Let X and Y be independently standard normal random variables and let Z = X^2$

Hi Im having a tough time with this question and cannot get

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