excans:542df9b17f: Difference between revisions
From Stochiki
(Created page with "'''Solution: D''' We have <math display = "block"> \begin{aligned} E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2) &= 2E(X^2) + E(X)^2 \\ &= \frac{2}{3} + \frac{1}{4} \\ &= \frac{11}{12} \end{aligned} </math>") |
mNo edit summary |
||
| Line 5: | Line 5: | ||
<math display = "block"> | <math display = "block"> | ||
\begin{aligned} | \begin{aligned} | ||
E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2) &= 2E(X^2) + | 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{ | &= \frac{7}{6} | ||
\end{aligned} | \end{aligned} | ||
</math> | </math> | ||
Latest revision as of 00:46, 28 June 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]]