Quiz 2, Stat 4158, Spring 2021 Time: 28 minutes (18 minutes to answer and 10 minutes to scan and upload answers.) Instructions: This quiz is open book and notes. Answer the following questions with...

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Quiz 2, Stat 4158, Spring 2021 Time: 28 minutes (18 minutes to answer and 10 minutes to scan and upload answers.) Instructions: This quiz is open book and notes. Answer the following questions with full and clear explanations. Scan and upload your work as one pdf file. 1. Let Y1, . . . , Yn be a random sample from a normal distribution with mean 5 and unknown variance σ2. Thus, the population pdf is f(y|σ) = 1√ 2πσ e− 1 2σ2 (y−5)2 , −∞ < y=""><∞, σ=""> 0. (a) Considering σ as the parameter, give the likelihood function. Specify the argument and the domain of the function. (b) Obtain the maximum likelihood estimators of σ and σ2. (c) Derive a method of moments estimator of σ2. [You may use the identity: V (Y ) = E(Y 2)− {E(Y )}2.] (d) Can the method of moments estimator of σ2 yield a negative value? Can the MLE be negative?

quiz-2-23qwa5xk.pdf

Answered Same DayFeb 25, 2021

Answer To: Quiz 2, Stat 4158, Spring 2021 Time: 28 minutes (18 minutes to answer and 10 minutes to scan and...

Bolla V V Satyanarayana answered on Feb 26 2021

132 Votes

b)
d)
No, it was not possible to get negative value, if the yields are negative but variance always a positive value.
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We derrive Maximum Likelihood estimator
for
We apply Logarithms on both...

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Quiz 2, Stat 4158, Spring 2021 Time: 28 minutes (18 minutes to answer and 10 minutes to scan and upload answers.) Instructions: This quiz is open book and notes. Answer the following questions with...

Answer To: Quiz 2, Stat 4158, Spring 2021 Time: 28 minutes (18 minutes to answer and 10 minutes to scan and...

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