I am self studying and the following is a problem that I have very little idea of how to solve.
Suppose X1, X2, . . . are iid Bernoulli(p) random variables. For large n, what is the approximate distribution of $\ln{\left(\frac{p}{1-p}\right)}$, the log-odds in favour of $X_1=1$ versus $X_1=0$?
So far the only thing I know is that
$$\sqrt{n}(f(\bar{X}-f(\mu))) \rightarrow N(0,[f'(\mu)]^2\sigma^2) \space \text{as} \space n\rightarrow\infty$$ which is supposedly the delta method.
All I want to know is to have some guidance towards what to study in order to be able to solve this problem.
I appreciate your help and time.