ps2sol_F08

ps2sol_F08 - The Hong Kong University of Science and...

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The Hong Kong University of Science and Technology IS O M 111 - Business S tatistics Problem Sheet 2 Suggested Solutions 1. (a) 0.382 (b) 0.379 (c) 0.55 (d) They are not independent. 2. (a) 0.1 (b) 0.3375 (c) 0.3375 (d) The distribution of X is given by x 0 1 2 3 P(x) 0.1125 0.3375 0.3375 0.2125 (e) μ = 1.65, σ = 0.9367 (f) 0.4706 (g) 1 3. Stock A: Expected gain (ignoring dividends) for Stock A = $ (148.25-100) = $48.25 Stock B: Expected gain (ignoring dividends) for Stock B = $ (103.50-100) = $3.50 Stock A has higher expected gain. Note: Taking into account the dividends yields the same answer. 4. (a) Let C - complete the MBA G - score > 500 P( G ) = 0.41 (b) Probability the she will complete her MBA, given she scored 575 on the GMAT: P( C | G ) = 0.854 (c) Probability that she will graduate, given she scored 450 on the test: P( C | G ) = 0.593 5. Let x be the number of personal call. p = 3/10 = 0.3 n = 10 (a) E( x ) = 3 (b) SD( x ) = 1.449 Page 1 of 6 Assignment 2 Suggested Solutions
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(c) P( x < 1) = 0.1493 (d) P( x > 5) = 0.0475 (e) P( x = 3) = 0.2668 6. (a) P(Democratic) = 0.429 (b) P(HK Island) = 0.208 (c) P(N.T.West Democratic) = 0.0994 (d) P(N.T.East Liberal) = 0.232 (e) P(Democratic | Kowloon East) = 0.558 (f) W and D are dependent. (g) E and L are mutually exclusive. 7. (a) P( x = 3) = 0.3456 (b) E( y ) = 1.6 (c) Var ( y ) = 0.96 (d) P(end at fourth game) = 0.1552 (e) P(seven games have to be played) = 0.2765 8. (a) Check first possibility first: x 1 100+1000 100+500+2000 p( x 1 ) 0.2 0.8 E( x 1 ) = 0.2(1100) + 0.8(2600) = 2300 (b) Check second possibility first x 2 100+500+1000 500+2000 p( x 2 ) 0.2 0.8 E ( x 2 ) = 0.2(1600) + 0.8(2500) = 2320 (c) Check the first possibility first because the expected total cost is lower.
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ps2sol_F08 - The Hong Kong University of Science and...

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