Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential n! distribution with parameter A. (Do not enter combinations as (). Enter combinations using the formula (): = k!(n - k)! (a) What is the probability that all thirteen bulbs fail before time t? (b) What is the probability that exactly k of the thirteen bulbs fail before time t? (c) Suppose that twelve of the bulbs have lifetimes that are exponentially distributed with parameter 1 and that the remaining bulb has a lifetime that is exponentially distributed with parameter 8 (it is made by another manufacturer). What is the probability that exactly seven of the thirteen bulbs fail before time t?
Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential n! distribution with parameter A. (Do not enter combinations as (). Enter combinations using the formula (): = k!(n - k)! (a) What is the probability that all thirteen bulbs fail before time t? (b) What is the probability that exactly k of the thirteen bulbs fail before time t? (c) Suppose that twelve of the bulbs have lifetimes that are exponentially distributed with parameter 1 and that the remaining bulb has a lifetime that is exponentially distributed with parameter 8 (it is made by another manufacturer). What is the probability that exactly seven of the thirteen bulbs fail before time t?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 60CR
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Transcribed Image Text:Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential
n!
distribution with parameter A. (Do not enter combinations as (). Enter combinations using the formula ():
=
k!(n - k)!
(a) What is the probability that all thirteen bulbs fail before time t?
(b) What is the probability that exactly k of the thirteen bulbs fail before time t?
(c) Suppose that twelve of the bulbs have lifetimes that are exponentially distributed with parameter 1 and that the remaining bulb has a lifetime that is
exponentially distributed with parameter 8 (it is made by another manufacturer). What is the probability that exactly seven of the thirteen bulbs fail
before time t?
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