(a) Suppose Y1 is a gamma random variable with parameters 1 and and Y 2 is also a gamma random variable with parameters 2 and Assuming Y 1 and Y 2 are independent, use the moment generating function to find the density function of U Y 1 Y 2 (b) Suppose Y 1 , Y 2 , , Y n are Poisson random variables each with parameter Assuming Y 1 and Y 2 are independent, use the moment generating function to find the probability function for W Y 1 Y 2 Y n

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Question: (a) Suppose Y1 is a gamma random variable with parameters 1 and and Y 2 is also a gamma random variable with parameters 2 and

(a) Suppose Y1 is a gamma random variable with parameters ₁ and and Y₂ is also a gamma random variable with parameters ₂ and . Assuming Y₁ and Y₂ are independent, use the moment generating function to find the density function of U = Y₁ + Y₂.

(b) Suppose Y₁, Y₂, . . . , Y_n are Poisson random variables each with parameter . Assuming Y₁ and Y₂ are independent, use the moment generating function to find the probability function for W = Y₁+Y₂+ +Y_n.

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