Question: In each case below, calculate the expected value of the random variable (Y) : (a) (mathrm{E}(Y mid X)=2 x^{2}+3, f_{X}(x)=e^{-x} I_{(0, infty)}(x)). (b) (mathrm{E}(Y mid

In each case below, calculate the expected value of the random variable \(Y\) :

(a) \(\mathrm{E}(Y \mid X)=2 x^{2}+3, f_{X}(x)=e^{-x} I_{(0, \infty)}(x)\).

(b) \(\mathrm{E}(Y \mid \mathrm{X})=3 X_{1} X_{2}, \mathrm{E}\left(X_{1}ight)=5, \mathrm{E}\left(X_{2}ight)=7, X_{1}\) and \(X_{2}\) are independent.

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