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Central Limit Theorem

Let  be a random sample from a gamma distribution with known parameter α = 3 and unknown β > 0. In Exercise 4.2.14, we obtained an approximate confidence interval for β based on the Central Limit Theorem. In this exercise obtain an exact confidence interval by first obtaining the distribution of 

Exercise 4.2.14

Let X denote the mean of a random sample of size 25 from a gamma-type distribution with α = 4 and β > 0. Use the Central Limit Theorem to find an approximate 0.954 confidence interval for μ, the mean of the gamma distribution.

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