The cumulative distribution function for health care costs experienced by a policyholder is modeled by the function

The policy has a deductible of 20. An insurer reimburses the policyholder for 100% of health care costs between 20 and 120. Health care costs above 120 are reimbursed at 50%. Let [math]G[/math] be the cumulative distribution function of reimbursements given that the reimbursement is positive.

Calculate [math]G(115)[/math].

• 0.683
• 0.727
• 0.741
• 0.757
• 0.777

1. The igniter switch may need to be replaced at a cost of 60. There is a 0.10 probability of this.
2. The pilot light may need to be replaced at a cost of 200. There is a 0.05 probability of this.
3. The furnace may need to be replaced at a cost of 3000. There is a 0.01 probability of this.

Calculate the deductible that would produce an expected claim payment of 30

• 100
• At least 100 but less than 150
• At least 150 but less than 200
• At least 200 but less than 250
• At least 250

At a polling booth, ballots are cast by ten voters, of whom three are Republicans, two are Democrats, and five are Independents. A local journalist interviews two of these voters, chosen randomly.

Calculate the expectation of the absolute value of the difference between the number of Republicans interviewed and the number of Democrats interviewed.

• 1/5
• 7/15
• 3/5
• 11/15
• 1

An insurance company insures a good driver and a bad driver on the same policy. The table below gives the probability of a given number of claims occurring for each of these drivers in the next ten years.

The number of claims occurring for the two drivers are independent.

Calculate the mode of the distribution of the total number of claims occurring on this policy in the next ten years.

• 0
• 1
• 2
• 3
• 4

Suppose the claim frequency [math]N[/math] has a probability function defined recursively by

where [math]a\gt0[/math] and [math]k \geq 1 [/math]. Which of the following expressions equals the expected value of [math]N[/math]?

1. [math]a/(1-a)[/math]
2. [math]a [/math]
3. [math]a/(1-a^2)[/math]
4. [math]a^2/(1-a^2) [/math]
5. [math]1-a [/math]

Suppose [math]F(x)[/math] is a continuous cumulative probability distribution function with [math]\lim_{x\rightarrow 1}F(x)=1[/math] and [math]F(x)\gt0[/math] for all [math]x[/math]. For which of the following [math]g(x)[/math] is [math]F(g(x))[/math] also a cumulative probability distribution function?

• [math]x^2[/math]
• [math]\sqrt{|x| + 1} [/math]
• [math]e^{-x}[/math]
• [math](1 + e^{-x})^{-1}[/math]
• [math]1-\ln(1 + e^{-x})[/math]

An insurance company sells a one-year automobile policy with a deductible of 2. The probability that the insured will incur a loss is 0.05. If there is a loss, the probability of a loss of amount [math]N[/math] is [math]KN[/math], for [math]N = 1, . . . , 5 [/math] and [math]K[/math] a constant. These are the only possible loss amounts and no more than one loss can occur.

Calculate the expected payment for this policy

• 0.031
• 0.066
• 0.072
• 0.110
• 0.150

A large university will begin a 13-day period during which students may register for that semester’s courses. Of those 13 days, the number of elapsed days before a randomly selected student registers has a continuous distribution with density function [math]f(t)[/math] that is symmetric about [math]t = 6.5 [/math] and proportional to [math]1/(t + 1)[/math] between days 0 and 6.5.

A student registers at the 60th percentile of this distribution.

Calculate the number of elapsed days in the registration period for this student.

• 4.01
• 7.80
• 8.99
• 10.22
• 10.51