Variables with t and Chi-sq distributions

[musicgold]

Hi,

I wish to know if there are any naturally occurring variables that have a t-distribution or chi-distribution.

I know that test statistics such as the mean or the sum of a sample has a t-distribution, where as the variance of a sample takes the chi-distribution. What I am trying to understand is why these statistics take a particular distribution.

Thanks,

MG.

 

[EnumaElish]

Both are special cases of the normal distribution:

http://en.wikipedia.org/wiki/Student's_t-distribution#Related_distributions

http://en.wikipedia.org/wiki/Chi-square_distribution#Related_distributions