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1. Let X1, X2, . . . , Xn be a random sample from a distribution...

1. Let X1, X2, . . . , Xn be a random sample from a distribution with pdf f(x, θ) = 1 3θ 4 x 3 e −x/θ , where 0 < x < ∞ and 0 < θ < ∞. Find the maximum likelihood estimator of ˆθ.

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Answer #1

given that

we have to find MLE of THETA

now likelihood function is given by

now log-likelihood function is given by

Now MLE is given by

We were unable to transcribe this image

We were unable to transcribe this image

logL = -nlog3 - 4nlogo + 3 loge; - 1

We were unable to transcribe this image

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