4-11. Suppose f (x) = -k(3 − x), 0 ≤ x ≤ 3;

0 elsewhere.

What value of k makes f (x) a legitimate probability density function? Find the cumulative distribution function F(t). Using f (x), find P(1 ≤ X ≤ 2).

Using F(t), also find P(1 ≤ X ≤ 2).