Answer Happy

(a) (2 pts) Given a continuous random variable X with probability density function f(X), what are the expressions for the mean and variance of this variable? (b) (2 pts) Can the value of the probability density function (PDF) f(x) exceed 1? Why or why not? (c) (2 pts) Consider a random variable X that follows the uniform distribution between a and b, i.e. its PDF is equal to a constant c on this interval, and 0 otherwise. Derive c in terms of a and b.

(d) (2 pts) Derive the expected value of X in terms of a and b. Show all your steps. (e) (2 pts) Derive the cumulative distribution function F(X) on the interval a < X < b.