Test 4 Solutions

# Test 4 Solutions - STAT 230 Test#4 4:30 5:15 pm UW computer userid mark/32 A Name Student I.D Circle your section and time slot 1 McLeish(12:30 2

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STAT 230 Test # 4 Nov 13 , 2008 4 : 30 5 : 15 pm mark ____/ 32 A Name : Student I . D : UW computer userid : Circle your section and time slot : 1 . McLeish ( 12 : 30 ) 2 . McLeish ( 12 : 30 ) 3 . Freire ( 1 : 30 ) [ 12 ] 1 . Assume random variables X and Y have joint probability function as follows. x f x , y 012 0 0.2 0.3 0 y 2 0.05 0.2 0.25 [ 4 ] a . Find the marginal probability function of X . f x .25,.5,.25for x 0,1,2 [ 4 ] b . Find cov X , Y . E X 1, E Y 1, E XY 2 .2 4 .25 1.4 Cov X , Y 1 0.4 [ 4 ] c . Are X and Y independent? Why or why not? They are not independent since Cov X , Y 0.

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[ 6 ] 2 . The proportions of cats with blood types A,B, and AB respectively in a large population are .7, .2 and .1 respectively. Let X 1 , X 2 , X 3 denote the frequencies of these three types in a random sample of size 20 taken from the population. Find the conditional distribution of X 3 given X 1 12. For x 3 0,1,. ..,8 P X 3 x 3 | X 1 12 P X 3 x 3 , X 1 12 P X 1 12 f 12,8
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## This note was uploaded on 10/21/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.

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Test 4 Solutions - STAT 230 Test#4 4:30 5:15 pm UW computer userid mark/32 A Name Student I.D Circle your section and time slot 1 McLeish(12:30 2

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