1. Let $X_1, X_2, \dots, X_N$ are independent and identically distributed uniform random variables in the\ninterval $(a, b)$, i.e., each has probability density function (pdf) and cumulative distribution\nfunction (cdf) given, respectively, by\n$\qquad f_x(x) = \begin{cases} \frac{1}{b-a}, & a \le x \le b\\ 0, & \text{otherwise} \end{cases}$ and $F_x(x) = \begin{cases} 0, & x \le a\\ \frac{x-a}{b-a}, & a < x < b\\ 1, & x \ge b \end{cases}$\n(a) Find the pdf of the maximum, $Y = \max(X_1, X_2, \dots, X_N)$.\n(b) Find the expectation $E[\max(X_1, X_2, \dots, X_N)]$.