Question

Let X and Y be joint continuous random variables with joint density function fpx, yq " # e ´y y 0 ă x ă y, 0 ă y ă 8 0 otherwise Compute ErX2 | Y " ys. Hint: Start with ErX2 | Y " ys " ż y 0 x 2 fX|Y px |

Answer 1

For X, the parameter

is λX = 1/2 and for Y it is λY = 1. Using the formula sheet, Mean is

E[Z] = E[X] + 2E[Y ] = 4. Variance is V ar(Z) = V ar(X) + 4V ar(Y ) = 8.