Probability question dealing with expected value shown below
a random variable X has a distribution ae^(ax), Let [x] denote the greatest integer function applied to the real number 𝑥, that is, the largest integer among those not exceeding 𝑥.
What is the correct expression for the expected value of 𝑁 =[x]? the answer should involve a
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how did you get (e^(a) 1)e^(a(w+1)) actually?

It's the derivative of 1−e ^(−a(w+1)). Chain rule.

if you simplify 1e^(awa) to 1(e^aw)(e^a) then the derivative with respect to w is (ae^(aw))(e^a) right? says the same thing on symbolab https://www.symbolab.com/solver/stepbystep/%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%5Cleft(1e%5E%7Baxa%7D%5Cright)?or=input

You’re right. I realized you can just find the PMF directly with an integral. I’ve edited my answer.

okay, thanks
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…should involve a what?
the constant a in the equation ae^(ax)