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4.2.4. Suppose we assume that X1, X2, . . . , Xn is a random sample from a (1, )
distribution.
(a) Show that the random variable (2/)
n
i=1
Xi has a
2
-distribution with 2n
degrees of freedom.
(b) Using the random variable in part (a) as a pivot random variable, nd a
(1 )100% condence interval for .
Hogg, Robert T; McKean, Joeseph; Craig, Allen T (2012-02-08). Introduction to Mathematical
Statistics (7th Edition) (Page 219). Pearson HE, Inc.. Kindle Edition.
Solution

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  • 1. 4.2.4. Suppose we assume that X1, X2, . . . , Xn is a random sample from a (1, ) distribution. (a) Show that the random variable (2/) n i=1 Xi has a 2 -distribution with 2n degrees of freedom. (b) Using the random variable in part (a) as a pivot random variable, nd a (1 )100% condence interval for . Hogg, Robert T; McKean, Joeseph; Craig, Allen T (2012-02-08). Introduction to Mathematical Statistics (7th Edition) (Page 219). Pearson HE, Inc.. Kindle Edition. Solution