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Unformatted text preview: APPM 4/5570 Solutions to Problems from Sections 3.6 and 4.1 82. P ( X = x ) = e Î» Î» x x ! = e . 2 . 2 x x ! , x = 0 , 1 , 2 , . . . a. P ( X = 1) = e . 2 . 2 1 1! = e . 2 (0 . 2) â‰ˆ . 1637 b. P ( X â‰¥ 2) = 1 P ( X < 2) = 1 [ P ( X = 0) + P ( X = 1)] = 1 e . 2 h . 2 0! + . 2 1 1! i â‰ˆ . 01752 c. The probability that a disk does not contain a missing pulse is e . 2 . 2 0! â‰ˆ . 8187307531 . By independence, this probability for two disks is (0 . 8187307531)(0 . 8187307531) â‰ˆ . 6703 86. P ( X = x ) = e Î» Î» x x ! = e 5 5 x x ! , x = 0 , 1 , 2 , . . . a. P ( X = 4) = e 5 5 4 4! â‰ˆ . 1755 b. P ( X â‰¥ 4) = 1 P ( X < 4) = 1 [ P ( X = 0) + P ( X = 1) + P ( X = 2) + P ( X = 3)] = 1 e 5 h 5 0! + 5 1 1! + 5 2 2! + 5 3 3! i = 1 e 5 h 1 + 5 + 25 2 + 125 6 i â‰ˆ . 7350 c. E 3 4 X = 3 4 E [ X ] = 3 4 Â· 5 = 15 4 â‰ˆ 3 . 75 . 88. Assuming independence of diodes, if we let X be the number that fail, then X âˆ¼ bin (200 , . 01). (That is, X is binomial with parameters n = 200 and...
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 '08
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 Probability theory, Binomial distribution, dx, dy, eâˆ’Î» Î»x

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