3. Suppose the lifetimes of two light bulbs (Bulb A and Bulb B) are measured (in 1000 hours) by random variable X and Y, each having exponential distribution with parameter A equal to 0.2 and 0.9 respectively. Assume that X and Y are independent of each other. (a) What is the joint pdf of X and Y? (b) What is the probability that each light bulb lasts at most 1000 hours (Hint: You want to calculate P(X ≤ 1, Y ≤ 1)? (c) What is the probability that Bulb B lasts more than twice as long as Bulb A? (d) What is the probability that the total lifetime of the two bulbs is at most 2000 hours? (e) What is the probability that the total lifetime of the two bulbs is between 1000 and 2000 hours?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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3. Suppose the lifetimes of two light bulbs (Bulb A and Bulb B) are measured (in 1000 hours)
by random variable X and Y, each having exponential distribution with parameter A equal to
0.2 and 0.9 respectively. Assume that X and Y are independent of each other.
(a) What is the joint pdf of X and Y?
(b) What is the probability that each light bulb lasts at most 1000 hours (Hint: You want to
calculate P(X ≤ 1, Y ≤ 1)?
(c) What is the probability that Bulb B lasts more than twice as long as Bulb A?
(d) What is the probability that the total lifetime of the two bulbs is at most 2000 hours?
(e) What is the probability that the total lifetime of the two bulbs is between 1000 and 2000
hours?
Transcribed Image Text:3. Suppose the lifetimes of two light bulbs (Bulb A and Bulb B) are measured (in 1000 hours) by random variable X and Y, each having exponential distribution with parameter A equal to 0.2 and 0.9 respectively. Assume that X and Y are independent of each other. (a) What is the joint pdf of X and Y? (b) What is the probability that each light bulb lasts at most 1000 hours (Hint: You want to calculate P(X ≤ 1, Y ≤ 1)? (c) What is the probability that Bulb B lasts more than twice as long as Bulb A? (d) What is the probability that the total lifetime of the two bulbs is at most 2000 hours? (e) What is the probability that the total lifetime of the two bulbs is between 1000 and 2000 hours?
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