You integrated twice with respect to y...
y
Oh my mistake, but answer is the same as before.
Thank you @Daniel and @Mariusz, the mistake is mine. The integrand will not contain the pdf of y in the denominator, as I will multiply with the pdf of y while evaluating the outer Expectation operation. It works without that.
Underscore represents Blank it cannot be used in symbol names. Try removing all underscores
Blank
u_x // FullForm (* Pattern[u, Blank[x]] *) ux // FullForm (* ux *)
I made the changes, you have suggested. It now shows " Cloud: This computation has exceeded the time limit for your plan". Is there anything I can do about it?