Suppose that a random variable X follows a binomial distribution. Find the bias of each of...
Suppose that a random variable X follows a binomial distribution. Find the bias of each of the following estimators. Be sure to follow your computations enough to determine whether the estimator is biased or unbiased.
a. p̂ = (X+1)/(n+2)
b. p̂ = X2/n2
c. p̂ = X/n
Homework Answers
Here,
X ~ Binomial (n, p)
So, E(X) = n*p and Var(X) = n*p*(1-p)
a) 
So, 
is a biased estimator for p.
b) 
So,
is a biased estimator for p.
c) 
So,
is a unbiased estimator for p.
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