test3 - Test III Fall 2008 Introduction to Probability...

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Fall 2008 Test III Page: 1 of 2 Introduction to Probability Monday, October 27, 2008 STA 4321/5325 Instructions: Please turn of your cell phones. Please write all oF your answers on a separate sheet oF paper and make sure you have clearly labeled the problem corresponding to your answer. Absolutely no cheating. This test has a total oF 55 points. Name: Some Equations Poisson If X Pois( λ ), the pmf of X is p ( x )= λ x x ! e - λ Hypergeometric If X hypergeom( N,k,n ), the pmf of X is p ( x )= ( k x )( N - k n - x ) ( N n ) and E( X )= nk/N . Exponential If X exp( θ ), the pdf of X is f ( x )= ± 1 θ e - x/θ ,x 0 0 , else Gamma If X gamma( α, β ), the pdf of X is f ( x )= ± 1 Γ( α ) β α x α - 1 e - x/β ,x 0 0 , else Also, E( X )= αβ and var( X )= αβ 2 . 1 (3+4=7 points) Suppose that 60% of the toasters produced for Target are defective. If toasters are randomly purchased one at a time, ±nd the probability that: (a) Exactly two defective toasters are bought before a working toaster is bought. (b) At least two defective toasters are bought before the second working toaster is bought.
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test3 - Test III Fall 2008 Introduction to Probability...

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