320_hw5 - b. What is the probability that x is equal to 1...

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Economics 320: Homework The Poisson Distribution and Joint probability distributions. 1. In the World Cup soccer match, the average is 2.7 goals per game. In a particular game, let X be the number of goals. a. If you want to find the probability of x goals, should you use Binomial or Poisson, Why? b. What is the probability of at least one goal? c. What is the probability of more than three goals? d. Construct the probability distribution (graph) and describe its shape. 2. It is estimated that 0.5 Percent of the callers to the Customer Service department of Dell, Inc., will receive a busy signal. What is the probability that of today’s 1,200 callers at least 5 received a busy signal? 3. Consider the joint probability distribution for X and Y below: X 1 2 Y 1 0.3 0.2 2 0.25 0.25 a. Compute the marginal probability distributions for X and Y.
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Unformatted text preview: b. What is the probability that x is equal to 1 and Y is equal to 2? c. What is the probability that x is equal to 1 if Y is equal to 2? d. What is the expected value of X and the expected value of Y? e. Calculate the covariance of X and Y. f. Calculate the correlation of X and Y and describe what this means. g. Suppose there is a linear function of X and Y, g(x,y) = 6X + 0.25Y. Compute the mean and the variance for the linear function g(x,y). 4. For each of the following, assume X 1 , X 2 , X 3 ,……X 100 are 100 independent random variables with mean 10 and standard deviation 5. Find mean and variance of random variable Y defined in each of the following. a. Y = X 1 – 2X 2 b. Y=(X 3-10)/5 c. 100 ) ... ( 100 2 1 x x x Y + + =...
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This homework help was uploaded on 04/22/2008 for the course ECON 320 taught by Professor Martin during the Spring '08 term at Allegheny.

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