An individual taken from a very large biological population is of type A with probability p=0.5(1+t) and of type B with probabiliy 1-p=0.5(1-t).
a) Suppose that X denotes the number of type A individuals in a random sample of size n. What is the probability that X = x?
My answer: Classic binomial situation.
b)Find the maximum likelihood estimator of t and show that it is unbiased.
My answer: Find log likelihood, differentiate yields
setting to zero yields t=(2x-n)/n
To show unbiased, I need to find E(t). This is an integral including which I have no idea how to integrate.
Thanks for your help.