3. Suppose that the probability density function of $X$ is f(x) = 2x (-x^2), 0 x < ∞. Find the probability density function of Y = X^2, $f(y) =$ (3).

7. Let $X_1, \dots, X_n, X_{n+1}$ be a random sample from a normal population having an unknown mean $\mu$ and variance 1, and $\bar{X}_n$ be the average of the first $n$ variables. Then, the distribution of $X_{n+1} - \bar{X}_n$ is (8). If $\bar{X}_{200} = 5$, then the 95% confidence interval for $X_{201}$ is (9).