10_07ans - STAT 410 Examples for 10/07/2009 Fall 2009 1....

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STAT 410 Examples for 10/07/2009 Fall 2009 1. Suppose that company A and company B are in the same industry sector, and the prices of their stocks, $X per share for company A and $Y per share for company B, vary from day to day randomly according to a bivariate normal distribution with parameters μ X = 45, σ X = 5.6, μ Y = 25, σ Y = 5, ρ = 0.8. a) What is the probability that on a given day the price of stock for company B ( Y ) exceeds $33? Y has Normal distribution with mean μ Y = 25 and standard deviation σ Y = 5. P ( Y > 33 ) = - 5 25 33 Z P = P ( Z > 1.60 ) = 1 – Φ ( 1.60 ) = 1 – 0.9452 = 0.0548 . b) Suppose that on a given day the price of stock for company A ( X ) is $52. What is the probability that the price of stock for company B ( Y ) exceeds $33? Given X = 52, Y has Normal distribution with mean ( 29 X X Y Y μ σ σ ρ μ - + x = ( 29 45 52 6 . 5 5 8 . 0 25 - + = 30 and variance ( 29 2 Y 2 σ ρ 1 - = ( 29 2 2 5 8 . 0 1 - = 9 ( standard deviation =
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10_07ans - STAT 410 Examples for 10/07/2009 Fall 2009 1....

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