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Stat 5101, Fall 1999, (Geyer) Final Exam

# Stat 5101, Fall 1999, (Geyer) Final Exam - Up Stat 5101...

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Up: Stat 5101 Stat 5101 Final ExamDecember 20, 1999 Name Student ID Secret Code (if you want your final grade posted). The exam is closed book. You may two by 11 sheets of paper with formulas (or anything else) on it, but no other notes. You may use a calculator, but shouldn't need to. Put all of your work on this test form (use the back if necessary). Show your work or give an explanation of your answer. No credit for numbers with no indication of where they came from. The points for the questions total to 100. There are pages and 8 problems. A normal distribution table is on a separate sheet of paper. 1. [25 pts.] Suppose X and Y are independent and identically distributed normal random variables. Show that are independent random variables. Be careful to clearly explain your reasoning. 2. [30 pts.] Suppose X and Z are independent random variables and Suppose Y = X 2 + Z . a. Find the function of X that is the best predictor (BP) of Y , also called the best unbiased predictor (BUP).

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