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

F(x)=0, if x<1

F(x)=0.4, if 1≤x<3

F(x)=0.6, if 3≤x<5

F(x)=0.8, if 5≤x<7,

F(x)=1.0, if x≥7.

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

(b) Compute P(4<X≤7).