0
$\begingroup$

Suppose $a \ge 0$ is a parameter and $X_1$ is an uniform random variable in $[1,4]$ and $X_2$ is an uniform random variable in $[1/2,1]$. How to find the expected value of $\max\{5-X_1a, 3-X_2a,0\}$?

$\endgroup$
2
  • $\begingroup$ Do you mean a uniform random variables? $\endgroup$
    – JimB
    Mar 4 at 5:44
  • $\begingroup$ Yes. I updated my question $\endgroup$
    – Katatonia
    Mar 4 at 5:54
3
$\begingroup$

If the random variables have Uniform distributions, then the following finds the mean:

dist = TransformedDistribution[Max[5 - x1 a, 3 - x2 a, 0], 
  {x1 \[Distributed] UniformDistribution[{1, 4}], 
   x2 \[Distributed] UniformDistribution[{1/2, 1}]}];

Mean[dist]

Meatn of transformed random variable

$\endgroup$

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.