Mathematics 467/554 Fall, 2019 – Take-Home Portion of the Final Exam
You may use your notes, the textbook, and material I have placed on Blackboard for
assistance in answering these questions. You should not seek answers or assistance from
other sources, but you may ask me questions. You may use calculators but should not
use computer packages. In the event I need to make a correction, I will announce it on
Blackboard.
The take-home portion should be submitted when you take the in-class portion. DO
NOT FORGET TO BRING YOUR ANSWERS!!
The take-home portion is worth 25% of the final exam grade.
1. Suppose X has F -distribution with r1 = 5 and r2 = 8 degrees of freedom. Use Theorem
3.3.1 if you have the 7th edition and Theorem 3.3.2 if you have the 8th edition to find
E(X), E(X 2 ), V ar(X), E(Y ), E(Y 2 ), and V ar(Y ). If a quantity does not exist, say so
and justify.
2. Let X1 , X2 , …, Xn be a random sample from a gamma distribution with parameters
α = 1 and β = θ where θ > 0. Find the maximum likelihood estimator of θ.
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