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 Unemployed |
Number Unemployed |
1 | 1029 |
2 | 1686 |
3 | 2269 |
4 | 2675 |
5 | 3487 |
6 | 4652 |
7 | 4145 |
8 | 3587 |
9 | 2325 |
10 | 1120 |
Let x be a random variable indicating the number of months a person is unemployed.
a.
Construct an empirical discrete probability distribution for the random variable x.
Calculation:
The data in the first column represents the number of months employed and the data in the second column corresponds to the number of unemployed persons.
Here, the total number of unemployed persons is 26,975. The corresponding probabilities of the random variable x are obtained by dividing the number of months of unemployment (f) by total number of unemployed persons (N).
That is,
For example,
b.
Check whether the distribution is valid or not.
c.
Find the probability that a person is unemployed for the two months or less and the Unemployed for more than two months.
d.
Find the probability that a person is unemployed for more than six months.
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