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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 35E
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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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