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Let X1 and X2 be two independent random variables having gamma distribution with parameters α1 =...

Let X1 and X2 be two independent random variables having gamma distribution with parameters α1 = 3, β1 = 3 and α2 = 5, β2 = 1, respectively. We are interested in finding the distribution of Y = 2X1 + 6X2. A standard approach is to apply a two-step procedure as that in question 2. However, as we discussed in the class, if the MGF technique is applicable, then it would be preferred due to its simplicity.

(a) Find the MGF of Y = 2X1 + 6X2.

(b) From the MGF to identify the distribution of Y .

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