Question: Themomentgeneratingfunctionofa 2 d random variableis md(t) = (1 2t)d~2 for t < 1~2. Supposethat U and V are independent,with U 2 d1 and

Themomentgeneratingfunctionofa χ2 d random variableis md(t) = (1 − 2t)−d~2 for t < 1~2.

Supposethat U and V are independent,with U ∼ χ2 d1 and U + V ∼ χ2 d1+d2 . FromExercise3.45, mU+V (t) = mU(t)mV (t). Showthat V ∼ χ2 d2 .

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