The chi-squared distribution (sum of squares of independent standard normal random variables) and the Student t-distribution (a standard normal divided by the square root of a scaled independent chi-squared variable) are named distributions defined derivatively in terms of the normal distribution, with the chi-squared shown to be a special case of the Gamma distribution and the t-distribution converging to the standard normal as its degrees-of-freedom parameter grows. The multivariate normal (MVN) distribution generalizes the univariate normal to random vectors, defined by the property that every linear combination of its components is itself normally distributed; within an MVN, zero covariance between components implies independence, a converse that does not hold for general random variables. These distributions belong to probability theory, specifically the family of "named" distributions built on the normal, and underlie core methods in mathematical statistics (chi-squared tests, t-tests, and multivariate analysis).
The chi-squared distribution (sum of squares of independent standard normal random variables) and the Student t-distribution (a standard normal divided by the square root of a scaled independent chi-…