# Math Help - Tough t-distribution problem

1. ## Tough t-distribution problem

2. $\bar Y-\bar X\sim N(0,9\sigma^2/20)$

so ${\bar Y-\bar X\over 3\sigma/\sqrt{20}}\sim N(0,1)$

Both $\bar Y$ and $\bar X$ are independent of $S_X$.

And $3S^2_X/\sigma^2\sim\chi^2_3$ or $S^2_X/\sigma^2\sim\chi^2_3/3$.

Take the square root of this and take the ratio of the normal and the chi-square and you will have your t.