Question

Emily has a coin with P(H) = pi and Pete has a coin with P(H) = P2. Emily tosses her coin n times, and denote the number of heads by X. Now Pete tosses his coin X times. What should be the distribution of the number of heads that Pete gets? Try to answer this question from two different approaches.
(a) Answer this question by constructing suitable binomial experiments.
(b) Answer this question by direct calculation. This is a challenging task. Hint: Try to use the binomial expansion xkym-k = (x + y)", k k=o. which holds for ALL positive integers m and real numbers x, y.

Answer 1

Answer:

Attached is the solution.