Homework5 - HOMEWORK PROBLEMS #5 SOLUTIONS TO EVEN PROBLEMS...

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Unformatted text preview: HOMEWORK PROBLEMS #5 SOLUTIONS TO EVEN PROBLEMS 38. Y ∼ Bin 4, 1 3 (a) p(y ) = 4 y 1y 3 2 4−y 3 (b) P (Y ≥ 3) = P (Y = 3) + P (Y = 4) = 4 3 13 3 2 3 + 4 4 14 3 = 8 81 + 1 81 = 1 9 ≈ 0.11 4 (c) E (Y ) = 4 × 1 = 3 ≈ 1.33 3 1 (d) Var(Y ) = 4 × 3 × 2 = 8 ≈ 0.89 3 9 52. Y ∼ Bin(20, 0.7). Using the table on the back of the book we get: (a) P (Y ≥ 17) = 1 − P (Y ≤ 16) = 1 − 0.893 = 0.107 (b) P (Y < 15) = P (Y ≤ 14) = 0.584 60. Y ∼ Bin(20, 0.8). Using the table on the back of the book we get: (a) P (Y = 14) = P (Y ≤ 14) − P (Y ≤ 13) = 0.196 − 0.087 = 0.109 (b) P (Y ≥ 10) = 1 − P (Y ≤ 9) = 1 − 0.001 = 0.999 (c) P (Y ≤ 16) = 0.589 (d) E (Y ) = 20 × 0.8 = 16 and Var(Y ) = 20 × 0.8 × 0.2 = 3.2 (e) P (14 ≤ Y ≤ 18) = P (Y ≤ 18) − P (Y ≤ 13) = 0.931 − 0.087 = 0.844 74. Y ∼ 78. Y ∼ P (Y P (Y 80. Y ∼ − Geo(0.9). So E (Y ) = 019 = 10 ≈= 1.11 and σ = 1p2p = . 9 Geo(0.6) = 5) = (0.4)4 (0.6) = 0.01536 ≥ 5) = P (Y > 4) = (0.4)4 = 0.0256 Geo 1 6 531 P (Y = 4) 6 6 = P (Y = 4|Y is even) = =∞ 2n−1 P (Y is even) 1 5 5 6 6 6 n=1 0.1 0.92 √ = f rac 109 ≈ 0.35. 5 6 1 6 3 1 6 5 6 2n−2 ∞ n=1 = 5 6 ∞ n=0 2 5 6 2n = 5 6 1 1− 2 = 52 6 275 ≈ 0.21 1296 1 ...
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This note was uploaded on 02/23/2011 for the course MATH 444 taught by Professor Any during the Fall '10 term at Roosevelt.

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