X₁ and X₂ are independent random variables having the standard normal distribution. Suppose Y₁ = X₁ and Y₂ = X₁ + X₂. Find the joint p.d.f. of Y₁ and Y₂. Find the mean and the variance of Y₂. If n independent random variables have the same gamma distribution with the pa- rameters a and ß, find the moment-generating function of their sum Y and find the p.d.f. of Y.

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