Question

An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X be the number of months between successive payments. The cumulative distribution function of X is ⎧ ⎪ ⎪ 0, if x < 1, ⎪ ⎪ ⎨ ⎪ 0.4, if 1 ≤ x < 3, F(x) = 0.6, if 3 ≤ x < 5, ⎪ ⎪ ⎪ ⎪ 0.8, if 5 ≤ x < 7, ⎩ ⎪

1.0, if x ≥ 7.

(a) What is the probability mass function of X?

(b) Compute P(4 < X ≤ 7).

Answer 1

a)

x	1	3	5	7
P(X)	0.4	0.2	0.2	0.2

b) P(4<x≤7) = P(X=5) + P(X=7) = 0.2+0.2 = 0.4