Let X = n-? 21Xbe the sample mean of a random sample X1,..., X, from the exponential distribution, Exp(0), with pdf f(1)

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Let X N 21xbe The Sample Mean Of A Random Sample X1 X From The Exponential Distribution Exp 0 With Pdf F 1 1 (42.01 KiB) Viewed 82 times

Let X = n-? 21Xbe the sample mean of a random sample X1,..., X, from the exponential distribution, Exp(0), with pdf f(1) = (1/0) exp{-x/0}, 2 > 0. (a) Show that E(X) = 0. The following (b), (c) and (d) are for graduates only. (b) Using the mgf technique determine the distribution of X. (Hint: See $5.2.3.) (c) Use (b) to show that Y = 2nX/0 has a x2 distribution with 2n degrees of freedom. (d) Based on (c), find a 95% confidence interval for 0 if n = 10. (Hint: Find c and d such that P(c