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Method of Moments Estimator and Maximum Likelihood Estimator

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June 15th, 2023

Let X1,…Xn be independent and identically distributed with pdf

f(x|theta)=(theta)x^(theta-1)
for 0 less than x less than 1 , =0 otherwise

i. Name the distribution above and its parameters.

ii. Find the method of moments estimator (MME) of theta by finding E(X) and setting it equal to Xbar and solve for theta.

iii. Find the maximum likelihood estimator (MLE) of theta.

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