Suppose that X is a random variable with the density: f(x) = (  θxθ−1  if      x ∈ (0, 1)              0         if     otherwise The parameter θ > 0 is to be estimated. Suppose that x1 = 0.3, x2 = 0.6 are the sample data. Get the estimate of θ (a) using the Moment Method; (b) using the Maximum Likelihood Method.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.