4-4. Let the cumulative distribution function for a random variable X appear as F(t) =

⎧⎪⎨

⎪⎩

0, t < 0;

2t − t2 0 ≤ t ≤ 1;

1, t > 0.

Find:

(a) P(X ≤ 1/4)

(b) P(X ≥ 1/4)

(c) P(1/3 ≤ X ≤ 3/4)

(d) The probability density function f (x)