Let $Y_1,Y_2,...,Y_N$ be a random sample from a distribution with probability density function $f_Y(y,\theta) = 2y/\theta^2$ if $0<y<\theta$ and $0$ otherwise.
(a) Show that $W = 3\bar{Y}/2$ is an unbiased estimator of $\theta$. (I think I got this one by getting the expectation of Y)
(b) What is the variance of W? (I am not quite sure how to work in this)
Thank you very much.
You can get the variance of $W$ from the variance of $Y$, and using the formulas that if $U$ and $V$ are independent random variables, and $\alpha$ is a constant, then $\text{Var}(U+V) = \text{Var}(U) + \text{Var}(V)$, and $\text{Var}(\alpha U) = \alpha^2 \text{Var}(U)$.