Let XiX2 Xn be a random sample from a gamma distribution wit

Let Xi,X2,... ,Xn be a random sample from a gamma distribution with mean 29 and variance 2theta2, where theta is an unknown positive real parameter. Show that 2/theta X,has a chi-squared distribution. Deduce that T = - 2/thetai=1 Xi has a chi-squared distribution with 4n degrees of freedom. Construct a 100(1 - alpha)% confidence interval for theta based on T. Obtain a 95% confidence interval for theta based on the following data4.0742272 1.3500102 2.5519888 3.0548888 4.1434620 2.7873961 6.9860217 3.0820517 12.0060020 5.8090500 13.7893878 1.9160152 0.6659256 0.8735431 5.6850480 4.6313874 3.8577010 1.5510683 6.3370545 4.9986028

Solution