I am having trouble with this homework question 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 11components 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 estimatedonce the latter has been.] (Round your answer to four decimal places.)Â =

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Answered: At time t= 0, 11 identical components…

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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The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
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The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years.a. If t represents time in years and y represents tooth size, usethe condition that y = 0.99y0 when t = 1000 to find thevalue of k in the equation y = y0ekt. Then use this value of kto answer the following questions.b. In about how many years will human teeth be 90% of theirpresent size?c. What will be our descendants’ tooth size 20,000 years fromnow (as a percentage of our present tooth size)?
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