Show that if Y1 has a 2 distribution with 1 degrees of freedom and Y2 has a 2

Chapter 6, Problem 6.59

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Show that if Y1 has a 2 distribution with 1 degrees of freedom and Y2 has a 2 distribution with 2 degrees of freedom, then U = Y1 + Y2 has a 2 distribution with 1 + 2 degrees of freedom, provided that Y1 and Y2 are independent.

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