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Unformatted text preview: and variance Var ( X Y ) = Var ( X ) + Var ( Y ) = 12 2 + 5 2 = 169 ( standard deviation = $13 ). P ( X Y < 0 ) = < 13 50 . 6 Z P = P ( Z < 0.50 ) = ( 0.50 ) = 0.3085 . b) (5) Alex buys 4 shares of Abitrisky, Inc. stock and 11 shares of Surething Corp. stock. What is the probability that the value of this portfolio will exceed $500? That is, find P ( 4 X + 11 Y > 500 ). 4 X + 11 Y has Normal distribution with mean E ( 4 X + 11 Y ) = 4 36.50 + 11 30.00 = $476 and variance Var ( 4 X + 11 Y ) = 16 Var ( X ) + 121 Var ( Y ) = 16 12 2 + 121 5 2 = 5329 ( standard deviation = $73 ). P ( 4 X + 11 Y > 500 ) = > 73 476 500 Z P = P ( Z > 0.33 ) = 1 ( 0.33 ) = 0.3707 ....
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 Spring '08
 Kim
 Statistics, Probability

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