Thanks for all the reply.
Why I think there is contradiction is because:
Let's say for the case of t distribution:
1.) If the sample size, n is small, it has fatter tail and larger variance. It is like I taking sample out of the large population to estimates the variance.
2.) If the...
I am new in statistic. I come across the sample variance calculation in a book and it explains that denominator is divided by n-1 instead of n is because variance in samples will be likely to be lower than the population variance, so we divide by n-1 to make the variance larger.
However, when...