Test 5 Solutions

# Test 5 Solutions - STAT 230 Test#5 4:30 5:20 pm mark/32 A...

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STAT 230 Test # 5 Nov 27 , 2008 4 : 30 5 : 20 pm mark ____/ 32 A Name : Student I . D : UW computer userid : Normal tables and summary of distributions on last page . Circle section and time slot : 1 . McLeish ( 12 : 30 ) 2 . McLeish ( 12 : 30 ) 3 . Freire ( 1 : 30 ) [ 9 ] 1 . Let X have a normal distribution with mean and variance 4. ( 3 )( a ) Obtain P X 11 , when 10. P X 11 P X 10 2 11 10 2 P Z 1 2 where Z is standard normal 1 .6915 0.3085 : ( 3 b ) Find such that P X 11 .9 0.9 P X 11 P X 2 11 2 P Z 11 2 Therefore 11 2 1.28 and solving 13.56 ( 3 ) c . Find c such that P | X | c .95 P | X | c P c X c P c 2 X 2 c 2 P Z c 2 .025 or F c 2 .975 From the table, c 2 1.96 and c 3.92

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[ 15 ] 2 . A continuous random variable X with probability density function (p.d.f.) f x x 1 x 1 0 0o t h e r w i s e where 0, is said to have a Pareto distribution. This distribution has many applications such as modeling the amount of insurance claims above a threshold value. [ 3 ] a . Find E X when 1. E X 1 x x 1 dx 1 1 x dx 1 [ 4 ] b . Find Var X . Is this always finite? E X 2 1 x 2 x 1 dx 1 1 x 1 dx 2 provided 2, otherwise Var X 2 1 2 This is finite only if 2.
1 .[ 4 ] c . Find the p.d.f. of Y ln X . For y positive, P Y y P ln X y P X e y 1 e y x 1 dx 1 e y Differentiating f Y y e y for y 0, and 0 otherwise.

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Test 5 Solutions - STAT 230 Test#5 4:30 5:20 pm mark/32 A...

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