ABSTRACT
FIGURE 3.3: The pdf graph of a chi-square distribution for various degrees of freedom k.
and its variance is
var(Y ) = 2kσ4. (3.34)
We now turn to the non-central chi-square distribution. Here, let Xi, i = 1, 2, . . . , k, be Gaussian distributed random variables with means µi and identical variances equal to σ2. The random variable Y =
∑k i X
2 i has the pdf
p(y) = 1
2σ2 (y s
)(k−2)/4 e−(s
(√ ys
σ2
) , y > 0, (3.35)
where the parameter s2, which is called the noncentrality parameter of the distribution, is given by
s2 = k∑ i=1
µ2i .
