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.

1.  What is the distribution of \(S_n\) ? Why ?
2. What is the distribution of  \(T_m\) ? Why ?
3. What is the distribution of \(S_n+T_m\) ? Why ?
4. Are \(S_n\) and \(T_m\) independent ? Why ?

[Pitman p. 159, # 10]