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Probability : Mean and Variance of a Distribution

Show that, if X has a U(0,1) distribution, its mean is 1/2 and its variance is 1/12.

Let Y = a + (b - a)X where a,b are constants, a<b. What is the distribution of Y? What are its mean and variance?

Please see attached for partial solution.


Solution Summary

The mean and variance of a distribution based on the U(0,1) distribution are calculated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.