Question

An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows: F(x) =0 - x < 10.33 - 1 < x < 30.44 - 3 < x < 40.48 - 4 < x < 60.86 - 6 < x < 121 - 12 < xa. What is the pmf of X? x 1 3 4 6 12p(x)b. Using just the cdf, compute P(3 ≤ X ≤ 6) and P(4 ≤ X).P(3 < X < 6) =P(4 < X) =

Answer 1

Explanation:

Given that X is the number of months between successive payments

Cumulative distribution function of X is

`F(x) =0, x<1\\F(x) = 0.33, 1<x<3\\F(x) =0.44, 3<x<4\\F(x) = 0.48, 4<x<6\\F(x) = 0.86, 6<x<12\\F(x) = 1, X>12\\`

a) PMF of x would be

`P(x) =0, x<1\\P(x) = 0.33, 1<x<3\\P(x) =0.11, 3<x<4\\F(x) = 0.04, 4<x<6\\F(x) = 0.38, 6<x<12\\P(x) = 0.14,\\ X>12`

b)
`P(3 ≤ X ≤ 6) =0.86-0.44=0.42\\ P(4 ≤ X)=1-0.44=0.56\\P(3 < X < 6) =0.6\\P(4 < X) =1-0.48=0.52`