Consider a random sample X_1, X_2, ... , X_n from the pdf  f(x; θ) = (θ+ 1)x^θ   0≤x≤1 where θ > −1   Use the Maximum Likelihood Method to obtain an estimator of θ and then compute the estimate for the following random sample of four observations: 0.42, 0.37, 0.64, and 0.55.

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 a random sample X_1, X_2, ... , X_n from the pdf 

f(x; θ) = (θ+ 1)x^θ   0≤x≤1 where θ > −1  

Use the Maximum Likelihood Method to obtain an estimator of θ and then compute the estimate
for the following random sample of four observations: 0.42, 0.37, 0.64, and 0.55.

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