Question: Consider an i.i.d. sample of random variables with density function f ( x ) = 2 2 x exp ( 2 x 2 ) a)

Consider an i.i.d. sample of random variables with density function

f(x)=22xexp(2x2)

a) find the method of moments estimate of for a sample X1,...,Xn from this distribution

b) find the maximum likelihood estimate of for a sample X1,...,Xn from this distribution

c) find the approx. variance of the maximum likelihood estimator and the variance of the method of moments estimator

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