I am working on a practice exercise in preparation for a final this week. I am really stuck on the following problem:
Let $X_1, X_2$ be a random sample for a population with the probability density function $$ f_k(x) = \left\{ \begin{matrix} {\displaystyle \frac{6x(k-x)}{k^3}} & \textrm{ if } 0 \leq x \leq k \\ \qquad 0 & \textrm{ else } \end{matrix} \right. $$ where $k>0$. Let $\hat{X} = X_1 + X_2$. Using $\hat{X}$ as an estimator, find the 90% confidence interval for $k$.
I am mostly looking for a place to start on the problem. I am not sure how to utilize what I know about estimators.