Let X1X2Xn be a random sample from a gamma distribution with

Let X_1,X_2,...,X_n be a random sample from a gamma distribution with mean 2 theta and variance 2theta^2,where theta is an unknown positive real parameter. Show that 2/theta X_i has a chi-squared distribution. Deduce that T = 2/theta summation i = 1 n X_i has a chi-squared distribution with An 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 data

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