(21) Consider the following potential probability density functions. Determine if they can be used as probability density functions and if so compute the mean, variance, and E(|x|)):

a. f (x) = cos(x) for −π ≤ x ≤ π, zero otherwise.

b. f (x) = sin(x) for 0 ≤ x ≤ π, zero otherwise.

c. f (x) = N−1 for 0 ≤ x ≤ N, zero otherwise.