Let Y₁ and Y₂ be a sample of n = 2 observations from a gamma random variable with parameters α = 1 and arbitrary β, and corresponding density function

Show that the sum W = (Y₁ + Y₂) is also a gamma random variable with parameters α = 2 and β. [Hint: You may use the result

Then use the fact that f(y₁, y₂) = f(y₁)f(y₂) since Y₁ and Y₂ are independent.]

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-y/B if y, > 0 (i = 1, 2) (y.) = elsewhere