# 05fin - Statistics 134, Sec 2, Fall 2005 FINAL EXAM Name:...

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Statistics 134, Sec 2, Fall 2005 Prof. Pitman FINAL EXAM Name: SID number: SHOW CALCULATIONS, OR GIVE REASONS, ON ALL PARTS OF ALL QUESTIONS. Numerical answers may be left unsimpliFed except where the question asks for a decimal or a fraction. You may refer to your text and notes. Please try not to interrupt the exam by asking questions. If you Fnd a question is ambiguous, indicate clearly how you choose to interpret it. You may interpret it to your own advantage to best demonstrate what you have learned in the course. Good luck! 1 2 3 4 5 6 7 8 9 10 Total

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1. A random variable X with values between -1 and 1 has probability density function f ( x ) = cx 2 for x in that range, for some constant c . a) Find c as a decimal. b) Give a formula for the cumulative distribution function of X . c) Find V ar ( X ) as a decimal. d) Let Y = X 2 . Find the probability density function of Y .
2. A multiple choice test has 4 possible answers for each question, exactly one of which is right. The test has 20 questions. A student knows the correct answer to 14 questions and guesses at random for the other 6. Let X be the number of questions the student gets right. a) Describe the distribution of

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## This note was uploaded on 10/02/2009 for the course STAT 87510 taught by Professor Jamespitman during the Spring '05 term at Berkeley.

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05fin - Statistics 134, Sec 2, Fall 2005 FINAL EXAM Name:...

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