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
Markgvanzalk
Answer
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Schwartstack
-
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 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
-
You’re right. I realized you can just find the PMF directly with an integral. I’ve edited my answer.
-
okay, thanks
- answered
- 605 views
- $10.00
Related Questions
- Wiener process probability
- Probability that a pump will fail during its design life
- Bivariate Normality questions
- Car accidents and the Poisson distribution
- How do we describe an intuitive arithmetic mean that gives the following? (I can't type more than 200 letters)
- Suppose that X is a random variable uniform in (0, 1), and define $M = 2 \max\{X, 1− X\} − 1$. Determine the distribution function of M.
- Number of different drinks that can be made using 6 ingredients
- Statistics- Probability, Hypotheses , Standard Error
…should involve a what?
the constant a in the equation ae^(-ax)