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 $\max\{5-X_1a, 3-X_2a,0\}$?

  • $\begingroup$ 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

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}]}];


Meatn of transformed random variable


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