Question

1. Find the maximum likelihood estimator (MLE) of θ based on a random sample X1, ....

1. Find the maximum likelihood estimator (MLE) of θ based on a random sample X1, . . . , Xn from each of the following distributions

(a) f(x; θ) = θ(1 − θ) ^(x−1) , x = 1, 2, . . . ; 0 ≤ θ ≤ 1

(b) f(x; θ) = (θ + 1)x ^(−θ−2) , x > 1, θ > 0

(c) f(x; θ) = θ^2xe^(−θx) , x > 0, θ > 0

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