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# Probability : Bayesian Statistics

Bayesian Statistics

The daily profit from a juice vending machine placed in an office building is a vlue of a normal random variable with unknown mean &#956; and variance &#963;2. Of course, the mean will vary somewhat from building to building, and the distributor feels that these average daily profits can best be described by a normal distribution with mean &#956;0 = \$30.00 and standard deviation &#963;0 = \$1.75. If one of these juice machines, placed in a certain building, showed an average daily profit of x = \$24.90 during the first 30 days with a standard deviation of s = \$2.10, find

(b) a 95% Bayesian interval of &#956; for this building;
(c) the probability that the average daily profit from the machine in this building is between \$24.00 and \$26.00.

#### Solution Summary

Probability and a Bayesian interval are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

\$2.19