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.)
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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![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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