4 Let theta 0 and let X1 X2 Xn be a random sample from a

4. Let theta > 0 and let X1, X2, ... , Xn be a random sample from a Uniform distribution on interval (0, theta). a) Obtain the method of moments estimator of theta, theta bar.

Solution

Here in this problem , expected or average value E(X) is :

E(X) = (0 + theta) / 2 = theta /2

Hence , the method of moment estimator of theta is calculated as :

E(X) = X-bar

=> theta/2 = X-bar

=> theta = 2X-bar

Thus, theta-cap = 2X-bar is a MOM estimator of theta.