Question: For independent random variables \(X\sim N\left( -2,7 \right)\) and \(Y\sim N\left( 3,1.4 \right)\) :

(a) Compute E(X) and var(X)

(b) In the scratchwork, sketch pdf(X) over the interval [-12, 81] and give coordinates of the peak

(c) For \(Z=4X-5Y\), compute E(Z) and \({{\sigma }^{2}}=\operatorname{var}\left( Z \right)\), and determine the distribution of Z

(d) Compute \(\Pr \left( 0\le X\le 3 \right)\)

(e) Compute \(\Pr \left( X\le 1 \right)\)

(f) Find the value of y that satisfies \(\Pr \left( X\le y \right)=0.9\)