4-22. Suppose a probability density function has the form f (x) =

⎧⎪⎪⎨

⎪⎪⎩

40+x 1600 , −40 < x < 0;

40−x 1600 0 ≤ x < 40;

0 elsewhere.

For A = {−10 ≤ X ≤ 10}, find P(A). (Hint: Write P(A) as the sum of two separate integrals for A = {x |−10 ≤ X ≤ 0} ∪ {0 ≤ X ≤ 10}.)