In a small metropolitan area, annual losses due to storm, fire, and theft are assumed to be mutually independent, exponentially distributed random variables with respective means 1.0, 1.5, and 2.4.

Calculate the probability that the maximum of these losses exceeds 3.

• 0.002
• 0.050
• 0.159
• 0.287
• 0.414

Claim amounts are independent random variables with probability density function

Calculate the probability that the largest of three randomly selected claims is less than 25.

• 8/125
• 12/125
• 27/125
• 2/5
• 3/5

A couple takes out a medical insurance policy that reimburses them for days of work missed due to illness. Let [math]X[/math] and [math]Y[/math] denote the number of days missed during a given month by the wife and husband, respectively. The policy pays a monthly benefit of 50 times the maximum of [math]X[/math] and [math]Y[/math], subject to a benefit limit of 100. [math]X[/math] and [math]Y[/math] are independent, each with a discrete uniform distribution on the set {0,1,2,3,4}.

Calculate the expected monthly benefit for missed days of work that is paid to the couple.

• 70
• 90
• 92
• 95
• 140

Losses follow an exponential distribution with mean 1. Two independent losses are observed.

Calculate the expected value of the smaller loss.

• 0.25
• 0.50
• 0.75
• 1.00
• 1.50

Losses in year 1 equal [math]X[/math] and have an exponential distribution with mean 1,000. Losses in year 2 equal [math]Y[/math] and, conditional on [math]X[/math], have an exponential distribution with mean [math]X[/math]. Determine the expected value of the maximum annual loss observed in the first two years of coverage.

• 735.76
• 1,103.64
• 1,367.88
• 1,500
• 2,103.64

The risk's claim frequency is uniform on {0,1} and the risk's claim size is uniform on [0,1000]. Determine the expected value of the maximum for a random sample of two losses.

• 225
• 1250/3
• 1750/3
• 500
• 2000/3