Let X 1 and X 2 be independent random variables Let X 1 and Y X 1 X 2 have chi square distributions with r 1 and r degrees of freedom, respectively Here r 1 r Show that X 2 has a chi square distribution with r r 1 degrees of freedom ...

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Let X 1 and X 2 be independent random variables. Let X 1 and Y = X

Question:

Let X₁ and X₂ be independent random variables. Let X₁ and Y = X₁+X₂ have chi-square distributions with r₁ and r degrees of freedom, respectively. Here r₁ < r. Show that X₂ has a chi-square distribution with r − r₁ degrees of freedom.