Question-38

Let \(X\) and \(Y\) be independent continuous random variables with exponential distributions: \(X \sim \text{Exp}(1)\) and \(Y \sim \text{Exp}(2)\). Find \(E[X \cdot Y]\), the expected value of the product of \(X\) and \(Y\).

Hint

Use the concept of independence as if \(X\) and \(Y\) are independent random variables, then \(E[XY] = E[X] E[Y]\)

Answer

0.5

Solution