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Unformatted text preview: Var ( X – Y ) = Var ( X ) + Var ( Y ) = 24 2 + 7 2 = 625 ( standard deviation = $25 ). P ( X – Y < 0 ) = < 25 5 Z P = P ( Z < – 0.20 ) = Φ ( – 0.20 ) = 0.4207 . b) (5) Alex buys 7 shares of Abitrisky, Inc. stock and 10 shares of Surething Corp. stock. What is the probability that the value of this portfolio will exceed $1000? That is, find P ( 7 X + 10 Y > 1000 ). 7 X + 10 Y has Normal distribution with mean E ( 7 X + 10 Y ) = 7 ⋅ 70 + 10 ⋅ 65 = $1140 and variance Var ( 7 X + 10 Y ) = 49 ⋅ Var ( X ) + 100 ⋅ Var ( Y ) = 49 ⋅ 12 2 + 100 ⋅ 5 2 = 33124 ( standard deviation = $182 ). P ( 7 X + 10 Y > 1000 ) = > 182 1140 1000 Z P = P ( Z > – 0.77 ) = 1 – Φ ( – 0.77 ) = 0.7794 ....
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This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Statistics, Probability

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