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Let Y be a random variable with an exponential distribution with E(Y) = 0, and supposed a single observation of Y wa aken from the population. ) Show that the pivotal legrees of freedom for this distribution? -) Using the pivotal quantity 2Y has a chi-square distribution using the moment generating function technique. What are th 2Y derive a 95% confidence interval for 0. ) Imagine an observation of Y= 1.5 was collected, compute the 95% confidence interval. Does this interval contain th

Let Y be a random variable with an exponential distribution with E(Y) = 0, and supposed a single observation of Y wa aken from the population. ) Show that the pivotal legrees of freedom for this distribution? -) Using the pivotal quantity 2Y has a chi-square distribution using the moment generating function technique. What are th 2Y derive a 95% confidence interval for 0. ) Imagine an observation of Y= 1.5 was collected, compute the 95% confidence interval. Does this interval contain th

Calculus For The Life Sciences
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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Let Y be a random variable with an exponential distribution with E(Y) = 0, and supposed a single observation of Y was taken from the population. a) Show that the pivotal 2Y has a chi-square distribution using the moment generating function technique. What are the degrees of freedom for this distribution? b) Using the pivotal quantity derive a 95% confidence interval for 0. c) Imagine an observation of Y = 1.5 was collected, compute the 95% confidence interval. Does this interval contain the population parameter? Explain your answer.
Transcribed Image Text:Let Y be a random variable with an exponential distribution with E(Y) = 0, and supposed a single observation of Y was taken from the population. a) Show that the pivotal 2Y has a chi-square distribution using the moment generating function technique. What are the degrees of freedom for this distribution? b) Using the pivotal quantity derive a 95% confidence interval for 0. c) Imagine an observation of Y = 1.5 was collected, compute the 95% confidence interval. Does this interval contain the population parameter? Explain your answer.
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