Problem

For each of the following distributions, derive formulas for the MLEs of the indicated par...

For each of the following distributions, derive formulas for the MLEs of the indicated parameters. Assume that we have IID data X1, X2, …, Xn from the distribution in question.

(a) U(0, b), MLE for b


(b) U(a, 0), MLE for a


(c) U(a, b), joint MLEs for a and b


(d) N(μ, σ2), joint MLEs for μ and σ


(e) LN(μ, σ2), joint MLEs for μ and σ


(f) Bernoulli(p), MLE for p


(g) DU(i, j), joint MLEs for i and j


(h) bin(t, p), MLE for p assuming that t is known


(i) negbin(s, p), MLE for p assuming that s is known


(j) U(θ – 0.5, θ + 0.5), MLE for θ

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Solutions For Problems in Chapter 6