In \(n+m\) independent \(\text{Bernoulli}(p)\) trials, let \(S_n\) be the number of successes in the first \(n\) trials and \(T_m\) number of successes in the last \(m\) trials.

- What is the distribution of \(S_n\) ? Why ?
- What is the distribution of \(T_m\) ? Why ?
- What is the distribution of \(S_n+T_m\) ? Why ?
- Are \(S_n\) and \(T_m\) independent ? Why ?

[Pitman p. 159, # 10]