Suppose that you have ten lightbulbs, that the lifetime ofeach is independent of all the other lifetimes, and that eachlifetime has an exponential distribution with parameter l.a. What is the probability that all ten bulbs fail beforetime t?b. What is the probability that exactly k of the ten bulbsfail before time t?c. Suppose that nine of the bulbs have lifetimes that areexponentially distributed with parameter l and thatthe remaining bulb has a lifetime that is exponentiallydistributed with parameter u (it is made byanother manufacturer). What is the probability thatexactly five of the ten bulbs fail before time t?

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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Suppose that you have ten lightbulbs, that the lifetime of
each is independent of all the other lifetimes, and that each
lifetime has an exponential distribution with parameter l.
a. What is the probability that all ten bulbs fail before
time t?
b. What is the probability that exactly k of the ten bulbs
fail before time t?
c. Suppose that nine of the bulbs have lifetimes that are
exponentially distributed with parameter l and that
the remaining bulb has a lifetime that is exponentially
distributed with parameter u (it is made by
another manufacturer). What is the probability that
exactly five of the ten bulbs fail before time t?

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