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Damages to a car in a crash are modelled by a random variable X, with density function k(x? - 60x + 800), 0

Damages to a car in a crash are modelled by a random variable X, with density function k(x? - 60x + 800), 0

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Damages to a car in a crash are modelled by a random variable X, with density function k(x? - 60x +800), 0<x< 20 0, Ax) otherwise where k is a constant. A particular car is insured with a deductible of 2. (i) Calculate the expected claim payment made by this car. (ii) This car was involved in a crash, given that the damages exceeded the deductible, find the probability that the damages exceeded 10. Two numbers are chosen independently and at random from the interval (0, 1). What is the probability that the two numbers differ by more than 0.5? As part of the underwriting process for insurance, each prospective policyholder is tested for high blood pressure. Let X represent the number of tests completed when the first person with high blood pressure is found. The expected value of X is 12.5. Find the probability that the sixth person tested is the second person with high blood pressure.
Transcribed Image Text:Damages to a car in a crash are modelled by a random variable X, with density function k(x? - 60x +800), 0<x< 20 0, Ax) otherwise where k is a constant. A particular car is insured with a deductible of 2. (i) Calculate the expected claim payment made by this car. (ii) This car was involved in a crash, given that the damages exceeded the deductible, find the probability that the damages exceeded 10. Two numbers are chosen independently and at random from the interval (0, 1). What is the probability that the two numbers differ by more than 0.5? As part of the underwriting process for insurance, each prospective policyholder is tested for high blood pressure. Let X represent the number of tests completed when the first person with high blood pressure is found. The expected value of X is 12.5. Find the probability that the sixth person tested is the second person with high blood pressure.
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