5
$\begingroup$

I'm looking for someone to walk me through how to solve E[ZW] if Z = max[X,Y] & W = min[X,Y]. X & Y are independent, uniform variables over the interval [0,1].

I solved E[Z] = 2/3 and E[W] = 1/3.

E[ZW] should equal 1/4 but I keep getting the wrong answer. I have searched the forums and used other people's answers to try and solve it but have gotten the incorrect numbers.

Thank you in advance!

$\endgroup$
9
$\begingroup$

Notice that $$\max(X,Y) \times \min(X,Y)= XY$$

Hence $$\mathbb{E}[ZW] = \mathbb{E}[XY]=\mathbb{E}[X]\mathbb{E}[Y]$$

$\endgroup$
5
$\begingroup$

Here's a hint: $ZW = XY$ no matter whether $Z > W$, $Z < W$, or $Z = W$.

$\endgroup$

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.