Solution
= Solution
Writing $S_n=\sum I_i$, each $\mathbb EI_i=1/n$. Distinct indicators have joint probability $1/[n(n-1)]$ and zero covariance, so $\mathbb ES_n=1$ and $\operatorname{var}S_n=n(1/n)(1-1/n)=1-1/n$.
= Solution
Writing $S_n=\sum I_i$, each $\mathbb EI_i=1/n$. Distinct indicators have joint probability $1/[n(n-1)]$ and zero covariance, so $\mathbb ES_n=1$ and $\operatorname{var}S_n=n(1/n)(1-1/n)=1-1/n$.