There are two coins, one with probability p1 of Heads and the other with probability p2 of Heads. One of the coins is randomly c
hosen (with equal probabilities for the two coins). It is then flipped n ≥ 2 times. Let X be the number of times it lands Heads. a) Find the PMF of X. b) What is the distribution of X if p1 = p2?
Since the coin is randomly chosen we can give the probability of choosing one or the other 0.5.
Now, X must be given by the probability of heads for either of the coins, since we do not know which coin have been choosed we must consider both of them, but multiplied by the 0.5 probability to choose one of them.
That is:
X = 0.5*(p1+p2)*n
a) If p1 = p2 = p
X = p*n
which makes sense since is the same as only having one coin
