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319handout5

# 319handout5 - (b Find the probability that the lifetime of...

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Econ 319, Fall 2008 TA: Simon Kwok Handout 5 1. Suppose the probability density function (pdf) of the joint distribution of X and Y is given by: f ( x; y ) = ° C (2 x + 3 y ) ; 0 ° x; y ° 1 0 ; otherwise : (a) Find the value of C: (b) Find the marginal distributions of X and Y . Are X and Y independent? (c) Find the cumulative distribution functions (cdf) of X and Y: (d) Find the conditional distributions of X j Y and Y j X: (e) Find Pr( X + Y < 1) : (f) Find Pr( X + Y > 1 : 5) : 2. Suppose that the lifetime X (in 1000 hours) of a certain brand of lightbulb produced in a certain factory is distributed according to the following pdf: f ( x ) = ° Ce ° 1 2 x ; x > 0 0 otherwise. (a) Find the constant
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Unformatted text preview: . (b) Find the probability that the lifetime of a lightbulb will be longer than 2000 hours. (c) Given that a lightbulb has been continuously lit for 2000 hours, what is the probability that it will last for at least another 2000 hours? (d) Suppose Simon bought 5 lightbulbs and he knows that their lifetimes are independently distributed. 1. What is the probability that at least one of them will burn out in less than 2000 hours? 2. What is the probability that more than two will burn out in less than 2000 hours? 1...
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