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 ?, that is, the largest integer among those not exceeding ?.
What is the correct expression for the expected value of ? =[x]? the answer should involve a

Probability
Markgvanzalk Markgvanzalk
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Schwartstack Schwartstack
  • Markgvanzalk Markgvanzalk

    how did you get (e^(a) -1)e^(-a(w+1)) actually?

  • Schwartstack Schwartstack

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

  • Markgvanzalk Markgvanzalk

    if you simplify 1-e^(-aw-a) 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/step-by-step/%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%5Cleft(1-e%5E%7B-ax-a%7D%5Cright)?or=input

  • Schwartstack Schwartstack

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

  • Markgvanzalk Markgvanzalk

    okay, thanks

The answer is accepted.