Chi-Squared Distribution -- from Wolfram MathWorld

If Y_i have normal independent distributions with mean 0 and variance 1, then chi^2=sum_(i=1)^rY_i^2 (1) is distributed as chi^2 with r degrees of freedom. This makes a chi^2 distribution a gamma distribution with theta=2 and alpha=r/2, where r is the number of degrees of freedom. More generally, if chi_i^2 are independently distributed according to a chi^2 distribution with r_1, r_2, ..., r_k degrees of freedom, then sum_(j=1)^kchi_j^2 (2) is distributed according to chi^2 with...