Past experience shows that over time the rivets in bridge supports can become dangerously loose. Assume that X, the number of loose rivets found per 10 feet beam on bridges over 20 years old, has the cumulative distribution shown in following table x 0 1 2 3 4 5 6 F(x) 0.05 0.15 0.35 0.65 0.85 0.95 1.0

Verify that f(x) = (6 - 2|x - 3|) /20 x = 1, 2, 3, 4, 5

and f(x) = (4 - |x - 3|) /20 x = 0 or 6