Thread: statistics_density

exam on Monday in this......please help!

Let Z~N(0,1) and let W~X{r} and let Z and W be independant.

Derive the density of the random variable

T = Z/sqrt(W/r)



Note: X is the chi symbol, r is a sub scribt and sqrt is square root

The standard way of proceeding in these cases is to write down the joint probability density of Z and X, integrate over the range of both subject to the condition that the function is constant with a new dummy variable.

Since Z varies from -inf to inf and X from 0 to inf, you have to do this kind of integration. Don't give up. The question implies that there is an answer. Perhaps you can find a useful substitution.