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Unformatted text preview: STAT 225 - Homework 7 Due Friday October 22 Comments: 1. This homework is due Friday, October 22 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must always show all work. If you do not show your work, you may not receive full credit. Do the following problems. 1. Show that if X ∼ U ( a, b ) then V ( X ) = ( b- a ) 2 12 . Guidance: Use the fact (which we proved in class) that E ( X ) = a + b 2 and apply the usual shortcut formula for variance of V ( X ) = E ( X 2 )- μ 2 Also it will be useful to know that a 3- b 3 = ( a- b )( a 2 + ab + b 2 ) 2. Page 177, problem 4.48 3. Page 176, problem 4.43 Guidance: Hopefully the following makes sense given what we have learned about variance: the shortcut variance formula also holds for functions g ( X ) of a random variable X . That is, V [ g ( X )] = E [ g ( X ) 2 ]- ( E [ g ( X )]) 2 4. A prison psychologist administers a profile test to the prison inmates. A prisoner is classified as “docile” if the score is less than 132 points, as “latently hostile” if the score is between 132...
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This note was uploaded on 05/16/2011 for the course STATISTICS 225 taught by Professor Finegold during the Spring '11 term at Carnegie Mellon.
- Spring '11