Let X bar be the mean of a random sample from the exponential distribution.

Let X bar be the mean of a random sample from the exponential distribution.

a) show that xbar is unbiasedpoint estimator of  θ

b) using the mgf technique,determine the distribution of xbar

c) use (b) to show that Y= 2nx bar/ θ has x^2 (chi) distibution with 2n degrees of freedom.

d) based on part (c),find a 95 % confidence interval for  θ if n=10