Assume there are two binomial experiments. For example, we coin a toss n times and get k heads. If we perform second experiment k number of times (depends on first experiment), how can we compute expectation of the combined experiments.
I think it would be sum of expectation of both experiments, for second one we can use formula for Conditional expectation.
How can one model such problems in general?
Also any references for understanding and approaching similar problems would be helpful