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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