Math Solutions

(See Solution) Consider an urn with three identical balls inside. The balls are identified by numbers 2,4 , and 6 . Present a table of the probability distribution

Question: Consider an urn with three identical balls inside. The balls are identified by numbers 2,4 , and 6 .

  1. Present a table of the probability distribution of experiment of selecting a ball from the urn at random and observing its number. Sketch the corresponding graph of the probability distribution. Calculate the mean and standard deviation of the distribution.
  2. Now suppose we select one ball from the urn at random, replace it inside the urn and repeat the process to select the second ball. The experiment generates nine equiprobable (equally likely) outcomes (2-2,2-4,2-6,4-2,4-4,4-6,6-2,6-4, and 6-6). The means of these nine outcomes are 2,3,4,3,4,5,4,5, and 6, respectively. Present the table of the probability distribution of the means. Sketch the corresponding graph of the probability distribution, and calculate the mean and standard deviation of the distribution of the means.
  3. Repeat part b if we select three random balls from the urn with replacement, one at a time.
  4. Compare and contrast the mean and the standard deviation calculated in part a with those calculated in parts b and c. Can you generalize your results? Explain. If you can generalize the results and without tabulating the outcomes, what are the mean and standard deviation of the means if we select 100 random balls from the urn with replacement, one at a time?
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    Solution: The downloadable solution consists of 6 pages
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