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The random variable X is distributed with pdf fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdf

fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0. (Please note the equation includes the term -(x/θ)2 )

a) What is the constant c?

b) We consider parameter θ is a number. What is MLE and MOM of θ? Assume you have an i.i.d. sample. Is MOM unbiased?

c) Please calculate the Cramer-Rao Lower Bound (CRLB). Compare the variance of MOM with Crameer-Rao Lower Bound (CRLB).

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