An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X 5 the number of months between successive payments. The cdf of X is as follows: F (x) 5 50 x, 1.30 1 # x, 3.40 3 # x, 4.45 4 # x, 6.60 6 # x, 12 1 12 # x a. What is the pmf of X? b. Using just the cdf, compute P (3 # X # 6) and P (4 # X).

The question is incomplete the correct question is:

An insurance company offers its policyholders a number of differentpremium payment options. For a randomly selected policyholder, letX=the number of months between successive payments. The cdf of X isas follows:

0 x<1

.30 1< x <3

F (x) =.40 3< x <4

.45 4< x <6

.60 6< x <12

1 12< x

a.) what is the pmf of x?

b.) using just the cdf, compute P (3< x <6) and P (4< x)

Answer: 0.175, 0.6

Step-by-step explanation:

In statistics tics, a probability mass function (PMF) is a function that shows the probability that a discrete random variable that is exactly equal to some value. It is also referred to as the discrete density function. The probability mass function is often the primary way of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.

The value of the random variable that have the largest probability mass is referred to as the mode.

PMF (X) =

x=1 0.15

x=2 0.15

x=3 0.10

x=4 0.025

x=5 0.025

x=6 0.025

x=7 0.025

x=8 0.025

x=9 0.025

x=10 0.025

x=11 0.025

x=12 0.4

b.) To compute P (3< x <6) andP (4< x) using just the cdf:

P (3< x <6) = P (x <6) - P (x<3)

=P (x < 6) + P (x = 6) - P (x<3)

= 0.45 + 0.025 - 0.3 = 0.175

P (4< x) = 1 - P (x < 4) = 1 - 0.4 = 0.6