Suppose that X is a continuous random variable with probability density of the form
f(x) =
1/x2 + kx 1 < x < 4
0 x otherwise
(a) Find the value of k.
(b) Calculate P[1 < X ? 2].
(c) Calculate P[X > 3].
(d) Compute E(X), the expected value of X.
(e) Compute the variance of X.
(f) Find the cumulative distribution function F(x) for the random variable X