ABSTRACT
Let X1, . . . , Xn be independent standard normal random variables. The distribution of
is called the chi-square distribution with degrees of freedom (df) n, and its probability density function is given by
f(x|n) = 1 2n/2Γ(n/2)
e−x/2xn/2−1, x > 0, n > 0. (11.1.1)
The chi-square random variable with df = n is denoted by χ2n. Since the probability density function is valid for any n > 0, alternatively, we can define the chi-square distribution as the one with the probability density function (11.1.1). This latter definition holds for any n > 0. An infinite series expression for the cdf is given in Section 11.5.1.
