Standard error with correlated observations

You average $n$ observations, each with variance $\sigma^2$, where every pair has correlation $\rho > 0$ (for example, the same-day returns of $n$ stocks).

(a) Find $\text{Var}(\bar{X})$.

(b) With $n = 100$ and $\rho = 0.1$, what is the effective sample size, meaning the number of independent observations that would give the same variance?

(c) What happens to the standard error as $n \to \infty$?