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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

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    You look for E(UY) where U and Y are independent. Does this ring any bell?2012-06-09

1 Answers 1