Revision as of 00:24, 28 June 2024 by Admin (Created page with "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>. '''References''' {{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}}")
ABy Admin
Jun 28'24
Exercise
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].
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.
ABy Admin
Jun 28'24
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]]