A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and 10,000 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business is assumed to have a Poisson distribution with mean 1.5.

Calculate the expected amount paid to the company under this policy during a one-year period.

• 2,769
• 5,000
• 7,231
• 8,347
• 10,578

A baseball team has scheduled its opening game for April 1. If it rains on April 1, the game is postponed and will be played on the next day that it does not rain. The team purchases insurance against rain. The policy will pay 1000 for each day, up to 2 days, that the opening game is postponed. The insurance company determines that the number of consecutive days of rain beginning on April 1 is a Poisson random variable with mean 0.6. Calculate the standard deviation of the amount the insurance company will have to pay.

• 668
• 699
• 775
• 817
• 904

The number of severe storms that strike city J in a year follows a binomial distribution with [math]n = 5 [/math] and [math]p = 0.6 [/math]. Given that [math]m[/math] severe storms strike city J in a year, the number of severe storms that strike city K in the same year is [math]m[/math] with probability 1/2, [math]m+1[/math] with probability 1/3, and [math]m+2[/math] with probability 1/6.

Calculate the expected number of severe storms that strike city J in a year during which 5 severe storms strike city K.

• 3.5
• 3.7
• 3.9
• 4.0
• 5.7

A multiple choice exam is given. A problem has four possible answers, and exactly one answer is correct. The student is allowed to choose a subset of the four possible answers as his answer. If his chosen subset contains the correct answer, the student receives three points, but he loses one point for each wrong answer in his chosen subset. Determine his expected score if he just guesses a subset uniformly and randomly.

• 0
• 0.5
• 1
• 1.5
• 2

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.