# Question: suppose that x1 xn are a...

###### Question details

Suppose that x1, . . . , xn are a random sample of lifetimes for individuals diagnosed with a certain disease. Assume a model with f(x; λ) = k(x/λ)^k−1 * e^−(x/λ)^k /λ, x > 0, where k is fixed and known. Interest is in the parameter

ζ = P(X > 25; λ) which gives the probability that an individual will survive more than 25 years with the disease. It can be shown that the cumulative distribution is F(x; λ) = P(X ≤ x; λ) = e^−(x/λ)^k .

1. Determine the MLE of ζ.