QZ 6-C - and variance Var ( X Y ) = Var ( X ) + Var ( Y ) =...

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STAT 400 Fall 2011 Version C Name ANSWERS . Quiz 6 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. The price of Abitrisky, Inc. stock ( X ) varies from day to day according to normal distribution with mean $36.50 and standard deviation $12. The price of Surething Corp. stock ( Y ) also varies from day to day according to normal distribution with mean $30 and standard deviation $5. Assume the prices of the two stocks are independent. a) (5) Find the probability that on a given day, the price of Surething Corp. stock is higher than the the price of Abitrisky, Inc. stock. That is, find P ( Y > X ). P ( Y > X ) = P ( X – Y < 0 ). X – Y has Normal distribution with mean E ( X – Y ) = 36.50 – 30.00 = $6.50
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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 &lt; 0 ) = -&lt; 13 50 . 6 Z P = P ( Z &lt; 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 &gt; 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 &gt; 500 ) = -&gt; 73 476 500 Z P = P ( Z &gt; 0.33 ) = 1 ( 0.33 ) = 0.3707 ....
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