# why is the variance of t-distribution with 1 and 2 degrees of freedom undefined while these distributions can be drawn? [duplicate]

The variance of a t-distribution is given by df/(df-2), hence the t-distribution with 1 and 2 degrees of freedom have no defined variance. Yet these distributions do exist and can be drawn, so one would say that their variances can be calculated. I hope somebody can explain this without using too much mathematics, as my skills in mathematical statistics are poor.

## marked as duplicate by kjetil b halvorsen, usεr11852, John, mdewey, whuber♦Aug 18 '17 at 16:03

• When you "draw the distribution" are you drawing all of it? Or only the middle 99.something percent of it? It's not that part that makes the variance not-finite. The finiteness or otherwise of the variance is essentially to do with the way the tail behaves in the limit as the variable approaches $\infty$ and $-\infty$ – Glen_b Jan 12 '17 at 0:41