5102-Midterm-1-Practice-Problems

5102-Midterm-1-Practice-Problems - PRACTICE PROBLEMS FOR...

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Unformatted text preview: PRACTICE PROBLEMS FOR MIDTERM 1 STAT 5102-004 (1) What is a statistic? (2) Prediction intervals are wider than confidence intervals. Why? (3) A Bernoulli Y with mean has variance (1- ). How large a random sample guarantees that E | Y- | 2 . 01? Note that 0 a 1 implies 0 a (1- a ) 1 / 4. (4) Let Y 1 ,...,Y n iid N ( , 1). What n guarantees Pr( | Y n- | . 049) . 95. (5) Let Y 1 ,...,Y n iid N (0 , 2 ) with 2 unknown. Let = 1 2 . The density of each random variable is (2 )- 1 2 1 2 exp (- 1 2 y 2 ) . (a) Confirm that = n n i =1 Y 2 i is the mle for . (b) Find the mle 2 for 2 . (c) Confirm that n 2 2 2 ( n ). (6) Let Y Gamma( , ). Note that Y is positive with density, mean, and variance f ( y | , ) = ( ) x - 1 e- x E Y = Var Y = 2 . If = 1, then Y is an exponential random variable. Let Y 1 ,...,Y n iid exponential( ), and assume a gamma prior distribution for...
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This note was uploaded on 02/24/2011 for the course STAT 5102 taught by Professor Staff during the Spring '03 term at Minnesota.

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5102-Midterm-1-Practice-Problems - PRACTICE PROBLEMS FOR...

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