Find [math]E(X^Y)[/math], where [math]X[/math] and [math]Y[/math] are independent random variables which are uniform on [math][0, 1][/math].

• 0.6931
• 0.7131
• 0.7344
• 0.7544
• 0.775

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: A

For fixed [math]y \in [0,1][/math], we have [math]E[X^y] = \frac{1}{y+1}[/math] and thus

[[math]] E[X^Y] = \int_{0}^1 \frac{1}{y+1} \, dy = \log(2). [[/math]]