Need help on this difficult statistic problem tnx?

Question

2.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 sucessive payments. The cumulative distribution function of X is

F(x)= {0, if x<1,

0.4, if 1<=x<3,

0.6, if3<=x<5,

0.8, if5<=x<7,

1.0, ifx>=7.

a. What is the probability mass function of X?

b. Compute P(4<X<=7)

Answer 1

a. probability mass function

f(x)   x

0.4  1

0.2  3

0.2  5

0.2  7

b. P(4&lt;X&lt;=7) = 0.2 +0.2 = 0.4

Why??

f(x) is probability; f(5) = 0.2, f(7) = 0.2