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Suppose that Y 1 has a Gamma distribution with parameters = 3/4 and = 2 and that Y 2 has a Gamma distribution with parameters

Suppose that Y1 has a Gamma distribution with parameters = 3/4 and = 2 and that Y2 has a Gamma distribution with parameters = 7/4 and = 2. Suppose further that Y 1 and Y2 are independent. Use moment generating functions to show that the random variable U= Y1 + Y2 has a chi-square distribution and determine its degrees of freedom

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