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Q12Section A (Section A)12 of 60

Covariance and moments of linear transformation

Let XX and YY be random variables such that X∼N(1,2)X\sim N(1, 2) and P(Y=X2+1)=1P(Y = \frac{X}{2}+1) = 1. Let α=Cov(X,Y)\alpha = \mathrm{Cov}(X, Y), β=E(Y)\beta = E(Y) and γ=Var(Y)\gamma = \mathrm{Var}(Y). Then, the value of α+2β+4γ\alpha+2\beta+4\gamma equals

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