Need help on this statistics 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) the PMF of X is defined as the derivative of the CDF, which is given in the problem. If you plot the CDF, you&#039;ll see that basically the PMF will be zero everywhere, except at the particular values x=1, 3, 5, and 7. At these values, the derivative will be 0.4, 0.2, 0.2, 0.2, respectively.

(b) To compute the probability that X is between 4 and 7, one would integrate the PMF between (4,7]. Because we already have the CDF, the shortcut is to evaluate F(7) - F(4+).