Find the Cramér–Rao lower bound for the variance of an unbiased estimator of θ, based on a sample of size n for the following pdf: f(x)=θx θ−1 , 0 0. B. Find th

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A. Find the Cramér–Rao lower bound for the variance of an unbiased estimator of θ,
based on a sample of size n for the following pdf: f(x)=θx
θ−1
, 0<x<1, θ > 0.

B. Find the Method of Moment estimator of θ in the above pdf.
C. Consider the following density function:
X -2 -1 0 1 2
f(x) 1/8 2/8 2/8 2/8 1/8
Find P(-1≤X≤1) (ii) F(X) (iii) P(X≤1.25) (iv) P(X>0)

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