16.3 Exercise 1

The pair $\left\{X , Y\right\} ci \left|\right. H$. $X \sim$ exponential $\left(u / 3\right)$, given $H = u$; $Y \sim$ exponential $\left(u / 5\right)$, given $H = u$; and $H \sim$ uniform $\left[1 , 2\right]$. Determine a general formula for $P \left(X > r , Y > s\right)$, then evaluate for $r = 3 , s = 10$.