Blocks of Bernoulli trials.
In n +m independent Bernoulli (p) trials, let Sn be the number of successes in the first n trials, Tm the number of successes in the last m trials.
a) What is the distribution of Sn? Why?
b) What is the distribution of Tm? Why?
c) What is the distribution of Sn + Tm? Why?
d) Are Sn and Tm independent? Why?