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

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Question: 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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