[Bayes' Theorem, Discrete Random Variables] It is known that 90% of new cars produced by a certain company have on average λ malfunctions per 1 km of covered distance. Besides this, it is known that remaining 10% of new cars were produced with a defect which increases the average malfunction rate to 21. The two types of cars are indistinguishable otherwise. When (a) Suppose that only a single malfunction has occured with a randomly selected car over 1,000 km of distance. What is the probability that the car is from the defective group, and how does it depend on X? (b) For a randomly selected car, find a minimum distance covered with no malfunctions for the probability that the car is from the non-defective group is 95% or above (express the result as a function of X).
[Bayes' Theorem, Discrete Random Variables] It is known that 90% of new cars produced by a certain company have on average λ malfunctions per 1 km of covered distance. Besides this, it is known that remaining 10% of new cars were produced with a defect which increases the average malfunction rate to 21. The two types of cars are indistinguishable otherwise. When (a) Suppose that only a single malfunction has occured with a randomly selected car over 1,000 km of distance. What is the probability that the car is from the defective group, and how does it depend on X? (b) For a randomly selected car, find a minimum distance covered with no malfunctions for the probability that the car is from the non-defective group is 95% or above (express the result as a function of X).
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![[Bayes' Theorem, Discrete Random Variables] It is known that 90% of new cars produced by a
certain company have on average À malfunctions per 1 km of covered distance. Besides this, it is
known that remaining 10% of new cars were produced with a defect which increases the average
malfunction rate to 2λ. The two types of cars are indistinguishable otherwise. When
(a) Suppose that only a single malfunction has occured with a randomly selected car over 1,000
km of distance. What is the probability that the car is from the defective group, and how does
it depend on λ?
(b) For a randomly selected car, find a minimum distance covered with no malfunctions for the
probability that the car is from the non-defective group is 95% or above (express the result as
a function of X).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F163cf53f-c0ce-4d67-85c3-58ee5a13e2c6%2Fc4c9075d-34d6-431c-9374-ba2b01de9f3e%2Fitwj4fk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[Bayes' Theorem, Discrete Random Variables] It is known that 90% of new cars produced by a
certain company have on average À malfunctions per 1 km of covered distance. Besides this, it is
known that remaining 10% of new cars were produced with a defect which increases the average
malfunction rate to 2λ. The two types of cars are indistinguishable otherwise. When
(a) Suppose that only a single malfunction has occured with a randomly selected car over 1,000
km of distance. What is the probability that the car is from the defective group, and how does
it depend on λ?
(b) For a randomly selected car, find a minimum distance covered with no malfunctions for the
probability that the car is from the non-defective group is 95% or above (express the result as
a function of X).
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