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MLE of P(X<2) - Exponential distribution

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the MLE of θ = P (X≤ 2) in a random sample of size n selected from an exponential distribution EXP(λ)

    2. Relevant equations

    f(x, λ) = λ e^(-λx)
    F(x, λ) = 1 - e^(-λx)

    3. The attempt at a solution
    I know how to find the MLE of the mean of an exponential distribution. But I am not sure how I can tackle this problem.

    We know that P ( X≤ 2) = ∫f(x) 0,2 = F(4)

    How do I get to the Likelihood from here?

    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 21, 2012 #2

    Ray Vickson

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    Homework Helper

    Is the following statement of your problem correct? You observe n independent values of X and observe that m of them have {X < 2} (or {X <= 2}). From that, you want to estimate θ = P{X <= 2}. If that is truly the statement, what does the exponential distribution have to do with it? (Of course, if you want to estimate λ you need to know the distribution, but that is not what you said you want to estimate.)

    RGV
     
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