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Consider {5.8065, 7.7508, 1.6117, 6.2933, 5.4781} to be a random independent and identically distributed sample from a Gaussian distribution describing a random variable Y of unknown mean and variance. Derive the maximum likelihood estimator of the parameter θ such that P(Y < θ) = 0.99. Hint: You may use that for the standard normal variable Z ∼ N (0, 1), we have P(Z < θ0) = 0.99 for θ0 = 2.326.

Consider {5.8065, 7.7508, 1.6117, 6.2933, 5.4781} to be a random independent and identically distributed sample from a Gaussian distribution describing a random variable Y of unknown mean and variance. Derive the maximum likelihood estimator of the parameter θ such that P(Y < θ) = 0.99. Hint: You may use that for the standard normal variable Z ∼ N (0, 1), we have P(Z < θ0) = 0.99 for θ0 = 2.326.

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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Consider {5.8065, 7.7508, 1.6117, 6.2933, 5.4781} to be a random independent and identically distributed sample from a Gaussian distribution describing a random variable
Y of unknown mean and variance. Derive the maximum likelihood estimator of the
parameter θ such that P(Y < θ) = 0.99.
Hint: You may use that for the standard normal variable Z ∼ N (0, 1), we have P(Z <
θ0) = 0.99 for θ0 = 2.326. 

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