=+20.16. 18.18 1 Let X1 ,..., X ,, be independent, each having the standard normal distribution. Show that 2-X? + · · · +X2 has density 1

(20.46)

x(7 /2)- 1e -x /2 2"/25(n/2)

over (0, 0). This is called the chi-squared distribution with n degrees of freedom.