Show that if y, has a x² distribution with v₂ degrees of freedom and Y₂ has a ² distribution with v₂ degrees of freedom, then U = Y₁ + Y₂ has a x² distribution with v₁ + v₂ degrees of freedom, provided that Y₁ and Y₂ are independent. The moment-generating function for Y₁ is my, (t) = and the moment-generating
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