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If Z1 ~ [tex]\Gamma(\alpha1, \beta)[/tex] and Z2 ~ [tex]\Gamma(\alpha2, \beta)[/tex]; Z1 and Z2 are independent, then Z = Z1 + Z2 ~[tex]\Gamma(\alpha1+\alpha2,\beta)[/tex]. Hence show that [tex]W [/tex]~ [tex]\Gamma(k/2,1/2)[/tex]

Well i know how to do the first part, by just multiplying the moment generating function of the gamma. But i dont understand what the W is refering to in the second part of the question, am i supposed to use the fact that Chi^2 ~ [tex]\Gamma(1/2,1/2)[/tex]?

If so, do i just somehow put the k instead of a 1?

Any guidance would be appreciated :)

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# Chi-square problem

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