Independent random variables $X$ and $Y$ are such that $E(X^2)=4$, $E(Y^2)=20$, $\text{Var}(X)=10$, $\operatorname{Var}(Y)=11$. Find $E(3X-2Y)$.

Question

I know how to find the expected value $E(X)$ of a random variables but I don't know how the $E(X^2)$ is related to $E(X^2)$ when the $X$ variables are not given. Let's say if $X=x$ where $x=1,2,3,4$. Then I could be able to deduce both $E(X)$ and $E(X^2)$.

E(X^2) = E(X^2). (Written in your post. Are you asking how $E(X^2)$ and $E(Y^2)$ are related? — amWhy, Jun 02 '21 at 23:05
Use the fact that $Var(X) = E[X]^2 - E[X^2]$ and similar for $Y$ to find $E[X]$ and $E[Y]$ and then use the fact that $E[3X-2Y] = 3E[X]-2E[Y]$ — Vercingetorix, Jun 02 '21 at 23:11

score 0 · Answer 1 · edited Jun 02 '21 at 23:25

0

$10=\operatorname{Var}(X)=EX^{2}-(EX)^{2}=4-(EX)^{2}\leq 4$. So there are no such random variables!

edited Jun 02 '21 at 23:25

Bernard

175,478

answered Jun 02 '21 at 23:18

Kavi Rama Murthy

311,013

Independent random variables $X$ and $Y$ are such that $E(X^2)=4$, $E(Y^2)=20$, $\text{Var}(X)=10$, $\operatorname{Var}(Y)=11$. Find $E(3X-2Y)$.

1 Answers1