So I always thought of the Student t-distribution as having only 1 parameter, v, the degrees of freedom (as described by wikipedia). When I searched however on how to find the MLE of v I keep coming across questions mentioning mu and sigma as parameters as well. So
1) Is the Student-t Distribution a special case of some "t-distribution"'s family, maybe where mu=0 and sigma=1.
2) Is there such a thing as solely estimating an MLE for the degree of freedom. I.e. is there a closed form solution to the MLE of the degree of freedom parameter.