The Joint Density Function for a Pair of Random Variables

Essay

The joint density function for a pair of random variables X and Y is $f ( x , y ) = \left\{ \begin{array} { l l } C ( x + 1 ) & \text { if } 0 \leq x \leq 1 \text { and } 0 \leq y \leq 1 \\0 & \text { otherwise }\end{array} \right.$ (a) Find the value of C.(b) Find $P ( X + Y \leq 1 )$ .(c) Find $P ( X \leq 2 Y \leq 3 X )$ .