quiz_2_2007Fall

quiz_2_2007Fall - 920 from the table. (6) (a) (b) At rst, P...

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QUIZ #2 SOLUTION (1) (a) { 0 , 1 , 2 , 3 } (b) Hypergeometric. (2) (a) Not legitimate because the sum of probabilities exceeds 1. (b) Not legitimate because there is negative value for probability. (c) Legitimate. (3) (a) F ( x ) = R x 0 . 5 tdt = h t 2 4 i x 0 = x 2 4 , 0 x 2 (b) P ( . 5 x 1 . 5) = R 1 . 5 . 5 . 5 xdx = h t 2 4 i 3 / 2 1 / 2 = 9 16 - 1 16 = 8 16 . (c) F ( x ) = x 2 4 = . 5 x = 2. (4) (a) E ( X ) = 1 · 1 21 + 2 · 2 21 + ··· + 6 6 21 = 4 . 33. E ( X 2 ) = 1 · 1 21 + 2 2 · 2 21 + ··· + 6 2 6 21 = 21. (b) $1000 × X 2 (5) (a) Poisson. (b) X Pois (1) ,P ( X 2) = .
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Unformatted text preview: 920 from the table. (6) (a) (b) At rst, P ( X = x ) is given by, X=x 7.5 10 P(X=x) .65 .35 Using the formula, P ( X = x,Y = u ) = P ( Y = y | X = x ) P ( X = x ), Joint pdf is, X/ Y 1 1.5 2 7.5 .455 .195 10 .0175 .228 .105 (c) The marginal pm of Y is given by Y=y 1 1.5 2 P(Y=y) .473 .423 .105 1...
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