 It is true, however, that the joint cumulants of degree greater than two for any multivariate normal distribution are zero.For two random variables, "X" and "Y", not necessarily independent, the kurtosis of the sum, "X" + "Y", is
Note that the binomial coefficients appear in the above equation.The exact interpretation of the Pearson measure of kurtosis (or excess kurtosis) used to be disputed, but is now settled.