7. Let X, X, be a random sample with common pár 1 2 f(x) θ e-A,...

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7. Let X, X, be a random sample with common pár 1 2 f(x) θ e-A, x > 0,0 > 0, 0 elsewhere. (a) Find the maximum likelihood estimator of θ, denoted by (b) Determine the sampling distribution of θ (c) Find Eô) and Var(). (d) What is the maximum value of the likelihood function? θ .

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Answer 1

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(a) The likelihood function of θ-L(θ)-g? exp (-9(x1 + x2)) log-likelihood function of θ-1(0)-log L(θ)-2logθ-8(x1 + x2) dl(0)

The pdf of Y is 0 otherwise 20 exp(-t)dt, 20t or,2y 0 2θ 2θ 2θ 2v2 Var@) = E(ё2)-e?(0) = 2、12 _ 층 0 82 (d) The marimum value

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