Let X1,X2,X3 be a random sample from a distribution with the probability density function f(xtheta)=begincasesfrac1theta e^-x/theta, & x0, 0, & otherwise,endcasesquadtheta0. If delta(X1,X2,X3) is an unbiased estimator of theta, which of the following CANNOT be attained as a value of the variance of delta at theta=1?

Q38Section B (Section B)38 of 60

Variances that an unbiased estimator cannot attain

Let $X_1,X_2,X_3$ be a random sample from a distribution with the probability density function

$f(x|\theta)=\begin{cases}\frac1\theta e^{-x/\theta}, & x>0,\ 0, & \text{otherwise,}\end{cases}\quad\theta>0.$

If $\delta(X_1,X_2,X_3)$ is an unbiased estimator of $\theta$ , which of the following CANNOT be attained as a value of the variance of $\delta$ at $\theta=1$ ?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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