 # t distribution Question

Which of the following statements used to describe the student’s t distribution is least accurate? The student’s t distribution A) Involves two random variables B) Is less peaked than the normal distribution C) Is symmetric around its mean D) Has thinner tails than the normal distribution. The answer is D, which is obviously an incorrect statement as t-distribution is flatter and has fatter tails than the normal distribution. But I was surprised about A. What are the 2 random variables? Is df a random variable as well? Thx.

“for two independent samples from two normally distributed populations, the difference in means can be tested with a t-statistic.” i think the two independent samples are the two random variables?

Googled this out and A. seemed like an obscure bit of statistics to me http://mathworld.wolfram.com/Studentst-Distribution.html the relevant bit seemed to be: Let X be a normally distributed random variable with mean 0 and variance sigma^2 , let Y^2/sigma^2 = have a chi-squared distribution with degrees of freedom, and let and be independent. Then t = X(n^2) / Y is distributed as Student’s with degrees of freedom. Did not see that anywhere in the notes!!!

i guess when prob distributions are involved there are always RVs in play