Let x1 x2xn be a random sample from Binomial 1theta where 0

Let x₁, x₂,...,x_n be a random sample from Binomial (1,theta), where 0 less than or equal to theta less than or equal to 1. Find an unbiased estimator of (theta^2)(1-theta)

Solution

Using binomial distribution and unbiased estimator formula answer is -thetha(4thetha^2-7thetha+2)/(thetha-1)^2