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06 STAT HWB a - Dr Valerie R Bencivenga Economics 329...

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Dr. Valerie R. Bencivenga Economics 329 PRACTICE HOMEWORK #6B: RIGHT ANSWERS 1. INDEX CARD QUESTION (parts a and b), EXTRA CREDIT QUESTION (part c). 2.a. This function is not a pdf, because the area under this pdf does not equal one: 2 0 2 x dx 2 0 2 0 b. This function is a pdf, because 0 ) x ( f X for all x , and the area under this pdf equals one: 1 0 8 1 2 8 1 x 8 1 dx x 8 3 2 2 2 0 2 0 3 2 c. This function is a pdf because 0 ) x ( f X for all x, and the area under it equals one: (1/2) [ (1/2)(2 - 0) ] + (1/2) [ (1/2)(4-2) ] = 1. 1 1/2 0 2 4 ) x ( f X x 3. X Y 2 X 2 2 Y b b and X Y X Y b a b a a. 5 5 0 a , 1 b 1 X Y X 5 Y 0 5 -1 1 4 6 Y X b.   0 0 2 1 0 a , 2 1 b 2 1 X Y X 2 1 Y Y X 0 -1 -2 1 2
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c.   2 5 5 2 1 0 a , 2 1 b 2 1 X Y X 2 1 2 5 Y Y X 0 -1 3 1 7 5 d.   2 4 5 3 2 2 a , 3 2 b 3 2 X Y X 3 2 3 4 Y Y X 2 0 8 4 5 4.a. ) 6 . 20 , 4 . 12 ( N ~ X 2 ) 6 . 8 , 2 . 5 ( N ~ Y 2 7257 . ) 60 (. F ) 60 . Z ( P ) 60 . Z ( P 6 . 20 4 . 12 0 Z P ) 0 X ( P This is the area under   x f X to the right of zero. b. 7291 . ) 61 (. F ) 61 . Z ( P ) 61 . Z ( P 6 . 8 2 . 5 0 Z P ) 0 Y ( P This is the area under   y f Y to the right of zero. f Y (y) points of inflection f X (x) 0 5.2 12.4 33 13.8
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c. 5478 . ) 12 (. F ) 12 . Z ( P ) 12 . Z ( P 6 . 20 4 . 12 10 Z P ) 10 X ( P This is the area under   x f X to the right of 10. d. 2877 . 7123 . 1 ) 56 (. F 1 ) 56 . Z ( P 6 . 8 2 . 5 10 Z P ) 10 Y ( P This is the area under   y f Y to the right of 10. f Y (y) points of inflection f X (x) 5.2 10 33 12.4 13.8 e. 1379 . 8621 . 1 ) 09 . 1 ( F 1 ) 09 . 1 Z ( P 6 . 20 4 . 12 10 Z P ) 10 X ( P This is the area under   x f X to the left of 10. f. 0384 . 9616 . 1 ) 77 . 1 ( F 1 ) 77 . 1 Z ( P 6 . 8 2 . 5 10 Z P ) 10 Y ( P This is the area under   y f Y to the left of 10. f
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06 STAT HWB a - Dr Valerie R Bencivenga Economics 329...

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