To find the Maximum Likelihood Estimator, the professor require us to follow and note 4 steps:...

Question

Question

Suppose X1, X2, , Xn are iid with pdf f(x; θ) =-e-x/θ, 0く〈 oo, zero elsewhere. Find the MLE of P(X 〉 k), for some k > 0 (known).

To find the Maximum Likelihood Estimator, the professor require us to follow and note 4 steps:

1. find L(θ) = product of all the f(X_I, θ)

2. take ln(L(θ))

3. take d/dθ of ln(L(θ)) and set the derivative to 0

4. solve for θ

I did:

1) P(X > k) = 1-P(x <= k) = 1-integral of f(k) from 0 to k

2) find the function in terms of θ

But I'm not sure what to do with the θ function, as it doesn't have x_i and I'm not sure how to find L(θ) with what I have

Answer 1

Answer #1

Answer 2

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