it is a problem from my exam praperation sheet
Let $U$ , $Y$ be independent random variables. Here $U$ is uniformly distributed on $(0 , 1)$ . whereas $Y$ is $\frac{1}{4} \delta(0) + \frac{3}{4} \delta (1)$ . Let $X := UY$ .
(a)Find $E[X]$
(b)Graph $F$ and find $P \left( 0 \le X \le \frac{2}{3} \right)$
can any one tell me how to solve this problem? Thanks