hi ive just started learning estimators today (self-teaching), so i might need quite a bit of help
i have just started this question
''A coin is tossed n times and the number of heads, H is counted. The probability of a head is p. Show that an unbiased estimator of p is H/n''
I found the sampling distribution, P(H=h), because of binomial distribution and said:
P(H=h)= nCh * (p^h) * (1-p) ^(n-h)
and i then said that E(estimator)=SIGMA { h/n*P(H=h) } from h=o to h=n.
I was given the result SIGMA r^2* (nCr) *(p^r)* (1-p)^{n-r} and so used this to evaluate my expectation
and got E(estimator)=[(p^2)/h]*(n-1)^2 +(p/h)
if it is unbiased the answer should be p so where have i gone wrong?
cheers