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Econ 100 HW1.docx - Homework 1 1 Consider the following...

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Homework 1 1. Consider the following probability distribution a. List all the different samples of n=2 measurements that can be selected from this Population. Possible Samples: 1. 0,0 9. 4,0 2. 0,2 10. 4,2 3. 0,4 11. 4,4 4. 0,6 12. 4,6 5. 2,0 13. 6,0 6. 2,2 14. 6,2 7. 2,4 15. 6,4 8. 2,6 16. 6,6 b. Calculate the mean of each different sample. Mean of each Sample ( ? ): ̅ 1. (0+0)/2=0 9. (4+0)/2=2 2. (0+2)/2=1 10. (4+2)/2=3 3. (0+4)/2=2 11. (4+4)/2=4 4. (0+6)/2=3 12. (4+6)/2=5 5. (2+0)/2=1 13. (6+0)/2=3 6. (2+2)/2=2 14. (6+2)/2=4 7. (2+4)/2=3 15. (6+4)/2=5 8. (2+6)/2=4 16. (6+6)/2=6 c. Of a sample of n=2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected? Probability of specific Sample: 1. 0,0= 1/6 9. 4,0= 1/6 2. 0,2= 1/6 10. 4,2= 1/6 3. 0,4= 1/6 11. 4,4= 1/6 4. 0,6= 1/6 12. 4,6= 1/6 5. 2,0= 1/6 13. 6,0= 1/6 6. 2,2= 1/6 14. 6,2= 1/6 7. 2,4= 1/6 15. 6,4= 1/6 8. 2,6= 1/6 16. 6,6= 1/6 d. Assume that a random sample of n=2 measurements is selected from a population. List the different values of ? and find the probability of each. Then give the sampling ̅ distribution of the sample mean ? in tabular form. ̅ Probability of ?
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