Let T=W / √(V / r), where the independent variables W and V are, respectively, normal with mean

Name: Let T=W / √(V / r), where the independent variables W and V are, respectively, normal with mean zero and variance 1 and chi-square with r degrees of freedom. Show that T^2 has an F -distribution with parameters r1=1 and r2=r. Hint: What is the distribution of the numerator of T^2 ?
Uploaded: 2022-11-07T21:03:50-08:00
Duration: 1 min 7 s
Channel: Caroline Mcclure
Description: Let T=W / √(V / r), where the independent variables W and V are, respectively, normal with mean zero and variance 1 and chi-square with r degrees of freedom. Show that T^2 has an F -distribution with parameters r1=1 and r2=r. Hint: What is the distribution of the numerator of T^2 ?

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Audrey Fong · Accepted Answer

First, we know that $W$ is normally distributed with mean 0 and variance 1. Therefore, $W^2$ has

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