Unformatted text preview: d) What is the name and parameters of the distribution of X? X has the binomial distribution with parameters n = 4 and π = ½, i.e., X ~ B(4, ½ ). e) Give reasons for your answer to part (e). i. There is a Bernoulli experiment with “Success” defined as selecting a family that has income above the median. ii. The experiment is repeated n = 4 times (selection of 4 families, assumed to be one at a time) iii. The repetitions are independent (random sampling guarantees that). iv. Probability of “Success” is ½ since the median divides the population units into two equal parts. v. The random variable of interest counts the number of “Success”s, i.e., families that have income above the median. Hence X has the binomial distribution with parameters n = 4 and π = ½, i.e., X ~ B(4, ½ )...
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- Fall '08
- Probability theory, Randomness, Household income in the United States, $34,200