Question: a random variable x can take the values 0 1...

A random variable X can take the values 0, 1 and 2 with P(X = 0) = 1−3α/4, P(X = 1) = α/2 and P(X = 2) = α/4 for some parameter α > 0. One observation is taken and we would like to estimate α.

i. Consider the estimators T1 = X and T2 = 2X2/3. Show that they are both unbiased estimators of α. (4 marks)

 

ii. Which of these estimators do you prefer and why? (6 marks)