2 Suppose Y1 Y2 Yn is a random sample of n independent

2. Suppose Y1 , Y2, . . . , Yn is a random sample of n independent observations from a distribution with pdf fY(y) = { . Determine the CRLB for the variance of unbiased estimators of theta when theta is sigma.

Solution

Consider the given distribution of yi

Variance of Y = E(Y^2) _ Mean^2

Mean = sigma rt (pi/2)

When theta = sigma

theta/rtn is the unbiased estimator for sigma