Question

Let (X, Y) be a random vector having the joint probability density function
$f(x,y)=\begin{cases} \frac{\sqrt2}{\sqrt{\pi}}e^{-2x}e^{-\frac{(y-x)^2}{2}}, & 0 <x< ∞,-∞<y<∞\\\ 0,& \text{otherwise} \end{cases}$
Then E(Y) equals

• A. $\frac{1}{2}$
• B. 2
• C. 1
• D. $\frac{1}{4}$

Answer 1

Answer: (A)

$\frac{1}{2}$

Answer 2

The correct option is (A) : $\frac{1}{2}$.