The problem statement:
Find the MLE of θ = P (X≤ 2) in a random sample of size n selected from an exponential distribution EXP(λ)
f(x, λ) = λ e^(-λx)
F(x, λ) = 1 - e^(-λx)
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, that was very helpful!
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