11ProbHw4sol

11ProbHw4sol - IEOR 3658 Probability Prof. Mariana...

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IEOR 3658 Assignment #4 Solutions Probability October 7, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #4 Solutions 1. Let S =$1000, r =0.1, p =0.05. Then the PMF of the total premium paid up to and including the first claim year is: P X ( x ) = (1 - p ) k p if x = S × 1 - (1 - r ) k r k = 0 , 1 ,... 2. P X ( x ) = 0 . 18 x = 0 0 . 27 x = 1 0 . 34 x = 2 0 . 14 x = 3 0 . 07 x = 4 3. (a) K = 1 2(1 2 +2 2 +3 2 ) = 1 28 (b) p Y ( y ) = ± y 2 14 , if x = 0 , 1 , 2 , 3 , 0 , otherwise , 4. P X ( x ) = Binomial(5 , 1 2 ,x - 2) = ² 5 x - 2 ³ ( 1 2 ) 5 , if x = 2 , 3 ,..., 7 5. The number of candy bars that you need to eat to find a ticket follows Geometric Distribution with parameter p . So the mean and variance are 1 p and 1 - p p 2 . 6. Let σ Y = p var( Y ), then (a) For Y = 4 X : E [ Y ] = E [4 X ] = 4 E [ X ] = 20 , var( Y ) = var(4 X ) = 16var( X ) = 144 , σ Y = 12 . And for
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This note was uploaded on 12/11/2011 for the course IEOR 3658 taught by Professor Olvera during the Fall '08 term at Columbia.

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11ProbHw4sol - IEOR 3658 Probability Prof. Mariana...

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