Suppose 100 samples of size n=3 are taken from each of the pdf's

(1) f_Y(y)=2y, 0\le{y}\le{1}
and
(2) f_Y(y)=4y^3, 0\le{y}\le{1}

and for each set of three observations the ratio

\frac{\bar{y}-\mu}{s/\sqrt{3}}

is calculated, where \mu is the expected value of the particular pdf being sampled. How would you expect the distributions of the two sets of ratio to be different? How would they be similar?


I know that the t-distribution is robust, so that it should be fairly unaffected by the underlying distributions unless they are extremely skewed and/or n is small. Clearly a sample of size three is fairly small, but how do I answer this question? I do not have software to automatically sample from these distributions to form a histogram and superimpose a t-distribution on top of it. Is there an easier way?