The density function of a random variable is given by f (x) = 2x(c + 1)

5 , 0 < x < 2.

The distribution function of X is

(a) F(t) =

⎧⎪⎨⎪⎩

0, t < 0, t∕2, 0 ≤ t < 2, 1, t ≥ 2

(b) F(t) =

⎧⎪⎨⎪⎩

0, t < 0, t2∕2, 0 ≤ t < 2, 1, t ≥ 2

(c) F(t) =

⎧⎪⎨⎪⎩

0, t < 0, t2∕4, 0 ≤ t < 2, 1, t ≥ 2

(d) F(t) =

⎧⎪⎨⎪⎩

0, t < 0, t∕4, 0 ≤ t < 2, 1 + t∕4, t ≥ 2

(e) F(t) =

⎧⎪⎨⎪⎩

0, t < 0, t∕5, 0 ≤ t < 2, 1, t ≥ 2