Show that if X , Y are two independent chi-square random variables
with m, n degrees of freedom, respectively, the random variables X +
Y and X/Y are independent.
(One-parameter exponential family) Let 0 be a real parameter. The
distribution of the random variable X having probability density function
/*(jc|0) = C(d)eQi*)T{x)h(x)
is said to belong to the exponential family of distributions. Show that
the gamma distribution, the normal distribution with known variance,
the normal distribution with known mean, and the binomial and Poisson distributions belong to the exponential family.