For a fixed θ>0, let X1,X2,…,Xn be i.i.d., each with the beta (1,θ) density. i) Find...

For a fixed θ>0, let X1,X2,…,Xn be i.i.d., each with the beta (1,θ) density.

i) Find θ^ that is the maximum likelihood estimate of θ.

ii) Let X have the beta (1,θ) density. Find the density of −log⁡(1−X). Recognize this as one of the famous ones and provide its name and parameters.

iii) Find f that is the density of the MLE θ^ in part (i).

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orchestra answered 1 year ago

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