Blocks of Bernoulli Trials

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]

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