\\ Let $Y_{1}, Y_{2}, \ldots, Y_{n} $ be a random sample from a Negative Binomial distribution with probability mass function given by $$ \mathrm{P] (\mathrm{y})=\left(\begin{array}{1} 2 \end{array} ight)\left(\frac{1} {\theta} ight)^{3}\left(1-\frac{1} {\theta} ight)^{(y-3)} \text { for } \mathrm{y}=3,4,5, \ldots. $$ Note that $\mathrm{E}(\mathrm{Y})=3 \theta$ and $\mathrm{V] (\mathrm{Y})=3 \theta^{2}\left(1-\frac{1} {\theta} ight) $. i.) Construct the likelihood function for the parameter $\theta$, and show that $U=\sum_{i=1}^{n} Y_{i}$ is a sufficient statistic for $\theta$. ii.) Find a Minimum Variance Unbiased Estimator for $\theta$. SP.DL.213