1
$\begingroup$

Consider discrete random variable $Y$ that takes value -1 with probability 0.5 and value 1 with probability 0.5. Given that $E(Y) = -1*0.5+1*.5 = 0$ and $E(Y^2) = -1^2*.5+1^2*.5 = 1$, I calculated that $Var(Y^2) = (E(Y^2))^2 - (E(Y))^4$.

Where am I wrong?

Improve this question
$\endgroup$
1
  • 2
    $\begingroup$ If this is a self-study question, please consider adding the corresponding tag. $\endgroup$
    – Igor F.
    Commented Mar 10, 2020 at 8:02

1 Answer 1

Reset to default
0
$\begingroup$

The identity you are using is $Var(X) = E[X^2] - (E[X])^2$, and in your case you are applying the identity with $X = Y^2$. So carefully plugging in you have $Var(Y^2) = E[Y^4] - (E[Y^2])^2$.

Since it looks like you know how to compute $E[Y^2]$ and $E[Y^4]$, you should be able to complete the exercise to show that $Var(Y^2) = 0$.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.