The question is to find the expected value and variance of $X - Y$ where $X, Y$ are independent random variables distributed in $[0,1]$

My Attempt:

The expected value is simple enough, where $E(X-Y) = E(X) - E(Y) = \frac{1}{2} - \frac{1}{2} = 0$.

The variance is where I'm running into issues,

$\mathrm{Var}(X-Y) = \mathrm{Var}(X) - \mathrm{Var}(Y) = \frac{1}{12} - \frac{1}{12} = 0$.

I don't know if the variance is set up correctly. Is there a step I am missing?

  • $\begingroup$ In addition to not having the variance equation correct, you did not establish that you were dealing with Uniformly distributed random variables. $\endgroup$ – Graham Kemp Apr 29 at 10:23

You have forgot to square the factors in front of the variables. For independent random variables $X,Y$ we have that $$\text{Var}(aX+bY)=a^2\text{Var}(X)+b^2\text{Var}(Y)$$ where you can use $a=1$ and $b=-1$ in your case.


$Var(X-Y)=Var(X)+Var(Y)-2Cov(X,Y)$. When are X and Y independent then $Cov(X,Y)=0$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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