solution02 - 2 x 1 17 = 1 giving x = 8 17 2 Section 2.2 2[3...

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Solution 02 1 Section 1.2 16. [2 points] 10 per cent. An example: 10 lost eye, ear, hand, and leg; 15 eye, ear, and hand; 20 eye, ear, and leg; 25 eye, hand, and leg; 30 ear, hand, and leg. 18. [2 points] (a) The right-hand side is the sum of the probabilities of all outcomes occurring in the left-hand side plus some more because of duplication. (b) 1 P ( A B ) = P ( A ) + P ( B ) - P ( A B ) . 22. [2 points] Ω = { 1 , 2 , 3 ,... } and the distribution is m ( n ) = (5 / 6) n - 1 (1 / 6). Now if 0 < x < 1, then X n =0 x j = 1 1 - x . Hence, 1 6 X n =0 ( 5 6 ) n - 1 = 1 / 6 1 - 5 / 6 = 1 . 26. [2 points] The probability that the two cards are of the same rank is 52 · 3 52 · 51 = 1 17 . Thus
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Unformatted text preview: 2 x + 1 17 = 1 giving x = 8 17 . 2 Section 2.2 2. [3 points] (a) C = 1 / 48. (b) P ( E ) = 1 96 ( b 2-a 2 ). (c) P ( X > 5) = 75 96 , P ( X < 7) = 45 96 . (d) P ( x 2-12 x + 35 > 0) = P ( x-5 > ,x-7 > 0) + P ( x-5 < ,x-7 < 0) = P ( x > 7) + P ( x < 5) = 3 4 4. [2 points] (a) .04, (b) .36, (c) .25, (d) .09. 6. [2 points] (a) e-. 01 T , (b) T = 100 log 2 = 69 . 3. 8. [3 points] (a) 1/8, (b) 1 2 (1 + log(2)), (c) .75, (d) .25, (e) 3/4, (f) 1/4, (g) 1/8, (h) π/ 8, (i) π/ 4. 12. [2 points] 1/4. 1...
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This note was uploaded on 11/15/2009 for the course STAT 311 taught by Professor Staff during the Fall '08 term at University of Wisconsin.

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