# Math Help - Stats exam help

1. ## Stats exam help

Let Z ~ N(0,1) and
Can anyone help with this question, have exam on saturday, each year we are asked to derive eithere the T - distribution

T = Z/ sqr(W/r) where Z ~ N(0,1) and W ~ X2( X SQUARED) , Z and W indep

The derivation the easy part but they ask questions on densities afterwards. Ill list a few below, Would really appreciate if anyone could help with any, test in a few hours and need a good grade to get my actuarial exemptions!

Q1: What kindof density does T2(T squared) have?

2. ## Re: Stats exam help

F(1,r)
and you left out the part where r is the df of the t.
Otherwise it's a multiple of a t.

$t^2={N^2(0,1)\over \chi^2/r}={\chi_1^2/1\over \chi_r^2/r}=F(1,r)$