Finding confidence intervals
I am working on a large problem that is broken down into steps. The goal is to find the 95% confidence interval for p(x=1).
X takes on the value 1 if unemployed, 0 otherwise.
Y takes on the value 1 if no response, 0 otherwise.
I have theta = pr(X=1), theta1= pr(X=1, Y=0) and theta2 = pr(Y=1).
I need to find estimators for theta 1 and theta 2 and prove they are unbiased given the following information.
We sent out n questionnaires. We received n1 back, and of that n1, m are unemployed.
My estimators are:
theta1hat = m/n1
theta2hat = (n-n1)/n
I am confused on how to show they are unbiased. I know to take the expectation, but don't know how to actually do that.
Thanks in advance.
Re: Finding confidence intervals
Just realized something, is this because it is the expected value of a constant?
My next step is to find the variance of theta1hat, which I assume is 0 because E(m^2/n1^2) - E(m/n1)2 = 0.
Are these assumptions correct?