squiz4 - 20 2 pairs of tomatoes There are exactly 10 × 10...

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Solutions to quiz # 4 (February 2) 1. Let F be the distribution function of X , so F ( a ) = P ( X a ). Hence F ( a ) = 0 if a < - 1 1 3 if - 1 a < 1 1 if a 1 . The graph of F is shown below. 0 1 -1 1 1/3 a 2. Let us introduce random variables X 1 , . . . , X 10 , where X k = b 1 if the k -th basket contains one red and one yellow tomatoes 0 otherwise. Then X = X 1 + . . . + X 10 and hence E ( X ) = E ( X 1 ) + . . . + E ( X 10 ) . Each basket is equally likely to contain any of
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Unformatted text preview: ( 20 2 ) pairs of tomatoes. There are exactly 10 × 10 pairs consisting of one red and one yellow tomato. Therefore, P ( X k = 1) = 10 · 10 ( 20 2 ) = 100 190 = 10 19 and E ( X k ) = 10 19 for k = 1 , . . . , 10 . Hence E ( X ) = 10 · 10 19 = 100 19 ≈ 5 . 26 . Answer: E ( X ) = 100 / 19. 1...
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