Part a If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short derivation. Part b Assume Var(X) = Var(Y). Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.
Part a If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short derivation. Part b Assume Var(X) = Var(Y). Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.
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.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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![Imagine you have two estimators X and Y, for unknown parameter µ. Assume that they are estimated from independent datasets. Let
Z = }(X+Y) be the average of these two estimators.
To write the symbol µ, you can write mu. For other math notation, you can E[X], Var(X) and (X+Y)/2 or (1/2)(X+Y).
Part a -
If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short
derivation.
Part bL
Assume Var(X) = Var(Y).
Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a7a892-d2a2-4a6f-a8a2-55ad3cac8d8b%2Fc4050b6c-c063-4277-9fc4-3659cd8c3832%2F1je657e_processed.png&w=3840&q=75)
Transcribed Image Text:Imagine you have two estimators X and Y, for unknown parameter µ. Assume that they are estimated from independent datasets. Let
Z = }(X+Y) be the average of these two estimators.
To write the symbol µ, you can write mu. For other math notation, you can E[X], Var(X) and (X+Y)/2 or (1/2)(X+Y).
Part a -
If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short
derivation.
Part bL
Assume Var(X) = Var(Y).
Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.
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