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 < 1 0.38, 1 <= x < 3 0.49, 3 <= x < 4 0.53, 4 <= x < 6 0.87, 6 <= x < 12 1, 12 <= x (a) What is the pmf of X? x | 1 | 3 | 4 | 6 | 12 p(x) | | | | | (b) Using just the cdf, compute P(3 <= X <= 6) and P(4 <= X). P(3 <= X <= 6) = P(4 <= X) =

          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 < 1
0.38, 1 <= x < 3
0.49, 3 <= x < 4
0.53, 4 <= x < 6
0.87, 6 <= x < 12
1, 12 <= x

(a) What is the pmf of X?
x | 1 | 3 | 4 | 6 | 12
p(x) | | | | | 

(b) Using just the cdf, compute P(3 <= X <= 6) and P(4 <= X).
P(3 <= X <= 6) =
P(4 <= X) =

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 < 1
0.38, 1 <= x < 3
0.49, 3 <= x < 4
0.53, 4 <= x < 6
0.87, 6 <= x < 12
1, 12 <= x

(a) What is the pmf of X?
x | 1 | 3 | 4 | 6 | 12
p(x) | | | | |

(b) Using just the cdf, compute P(3 <= X <= 6) and P(4 <= X).
P(3 <= X <= 6) =
P(4 <= X) =

Added by Carmen O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

03/31/2022

Step 1

We can find the pmf from the cdf (cumulative distribution function) by calculating the difference between consecutive cdf values. * **For x = 1:** p(1) = F(1) - F(0) = 0.38 - 0 = 0.38 * **For x = 3:** p(3) = F(3) - F(1) = 0.49 - 0.38 = 0.11 * **For x = 4:** p(4) Show more…

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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 < 1 0.38, 1 <= x < 3 0.49, 3 <= x < 4 0.53, 4 <= x < 6 0.87, 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).