For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of months unemployed and the values in the second column show the corresponding number of unemployed persons. Months Number Unemployed Unemployed 1029 1 1686 3 4 5 6 2269 2675 3487 4652 4145 3587 2325 1120 7 8 9 10 Let x be a random variable indicating the number of months a person is unemployed. a) Develop an empirical discrete probability distribution for x.

Enter all answers rounded UP to 4 decimal places, using a zero in front of the decimal if answers are less than 1 Months Unemployed f(x) 1 2 3 4 5 6 7 8 9 10 b) Does this probability distribution meet the requirements for a valid discrete probability distribution? Enter Yes or No to each requirment. Requirement 1 Requirement 2 space For the following questions, round your answer up to 4 decimal places, using a zero in front of the decimal if answers are less than 1. Unemployed 2 3 4 5 6 7 8 9 10 Unemployed 1029 1686 2269 2675 3487 4652 4145 3587 2325 1120 Let x be a random variable indicating the number of months a person is unemployed.

a) Develop an empirical discrete probability distribution for x. Enter all answers rounded UP to 4 decimal places, using a zero in front of the decimal if answers are less than 1 Months Unemployed f(x) 2 3 4 5 6 7 8 9 10 b) Does this probability distribution meet the requirements for a valid discrete probability distribution? Enter Yes or No to each requirment. Requirement 1 Requirement 2 space For the following questions, round your answer up to 4 decimal places, using a zero i front of the decimal if answers are less than 1.

c) What is the probability that a person is unemployed for two months or less?

d) What is the probability that a person is unemployed for more than two months?

e) What is the probability that a person is unemployed for more than six months?

QUESTION 3 The following table provides a discrete probability distribution for the random variable x. x f(x) 3 0.25 6 0.50 9 0.25 For the following questions, round your answers to 2 decimal places.

a) Calculate E(x), the expected value of x.

b) Calculate the variance of x.

c) Calculate the standard deviation of x. QUESTION 4 QUESTION 7 Consider a Poisson distribution with a mean of 3 For the following questions, round your answers to 4 decimal places, using a zero in front of the decimal for answers less than

1. a) Calculate f(2)

b) Calculate f(1)

c) Calculate P( x2)

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