I need help with this question. (a) A lamp has two bulbs, each of a type with average lifetime 1,500 hours. Assuming that we can model the probabilityof failure of a bulb by an exponential density function with mean μ = 1,500, find the probability that both of thelamp's bulbs fail within 1,600 hours. (Round your answer to four decimal places.)0.4301(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of thesame type, find the probability that the two bulbs fail within a total of 1,600 hours. (Round your answer to fourdecimal places.)0.3047X

a) Given that,There is a lamp with two bulbs, each of a type with an average lifetime of 1500…

of a type with average lifetime 1,500 hours. Assuming that we can n xponential density function with mean μ = 1,500, find the probability 00 hours. (Round your answer to four decimal places.) bulb of the same type as in part (a). If one bulb burns out and is repl ility that the two bulbs fail within a total of 1,600 hours. (Round your

of a type with average lifetime 1,500 hours. Assuming that we can n xponential density function with mean μ = 1,500, find the probability 00 hours. (Round your answer to four decimal places.) bulb of the same type as in part (a). If one bulb burns out and is repl ility that the two bulbs fail within a total of 1,600 hours. (Round your

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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(a) A lamp has two bulbs, each of a type with average lifetime 1,700 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean ? = 1,700, find the probability that both of the lamp's bulbs fail within 1,700 hours. (Round your answer to four decimal places.) (b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1,700 hours. (Round your answer to four decimal places.)
(a) A lamp has two bulbs, each of a type with average lifetime 1800 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean μ = 1800, find the probability that both of the lamp's bulbs fail within 1800 hours. (Round your answer to four decimal places.)(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1800 hours. (Round your answer to four decimal places.)
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a. Find the 50-th percentile of X. That is to say the value of x such that P (X ≤ x) = 0.5. b. Now say you have two independent jet engines. What is the probability that only one of themwill last more than 12 months before needing to be rebuilt? c. Find the probability density function f(x) by taking the derivative of F(x) with respect to x.
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Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 23 seconds. (a) Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket. f(x) = , x ≥ 0 , elsewhere (b) What is the probability that a customer will have to wait between 30 and 45 seconds? (Round your answer to four decimal places.) (c) What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places.)
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