At time t= 0, 11 identical components are tested. The lifetime distribution of each is exponential with parameter À. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y = 5 of the 11 components are still in operation (so 6 have failed). Derive the mle of A. [Hint: Let Y = the number that survive 24 hours. Then Y Bin(n, p). What is the mle of p? Now notice that p = P(X, 2 24), where X, is exponentially distributed. This relates i to p, so the former can be estimated once the latter has been.) (Round your answer to four decimal places.)
At time t= 0, 11 identical components are tested. The lifetime distribution of each is exponential with parameter À. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y = 5 of the 11 components are still in operation (so 6 have failed). Derive the mle of A. [Hint: Let Y = the number that survive 24 hours. Then Y Bin(n, p). What is the mle of p? Now notice that p = P(X, 2 24), where X, is exponentially distributed. This relates i to p, so the former can be estimated once the latter has been.) (Round your answer to four decimal places.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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![At time t = 0, 11 identical components are tested. The lifetime distribution of each is exponential with parameter a. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y = 5 of the 11
components are still in operation (so 6 have failed). Derive the mle of 1. [Hint: Let Y = the number that survive 24 hours. Then Y - Bin(n, p). What is the mle of p? Now notice that p = P(X; > 24), where X, is exponentially distributed. This relates 1 to p, so the former can be estimated
once the latter has been.] (Round your answer to four decimal places.)
 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86bfc21f-7304-4d6a-8ae3-de059a5180e7%2F2784d3f2-5ef7-4475-990b-fc997a9a9600%2F8bw1u2f_processed.png&w=3840&q=75)
Transcribed Image Text:At time t = 0, 11 identical components are tested. The lifetime distribution of each is exponential with parameter a. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y = 5 of the 11
components are still in operation (so 6 have failed). Derive the mle of 1. [Hint: Let Y = the number that survive 24 hours. Then Y - Bin(n, p). What is the mle of p? Now notice that p = P(X; > 24), where X, is exponentially distributed. This relates 1 to p, so the former can be estimated
once the latter has been.] (Round your answer to four decimal places.)
 =
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