Let [math]X[/math] and [math]Y[/math] be independent random variables with uniform density functions on [math][0,1][/math]. Find [math]E((X + Y)^2)[/math].

• 2/3
• 3/4
• 1
• 7/6
• 3/2

References

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

Solution: D

We have

[[math]] \begin{aligned} E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2) &= 2E(X^2) + 2E(X)^2 \\ &= \frac{2}{3} + \frac{1}{2} \\ &= \frac{7}{6} \end{aligned} [[/math]]