A biased coin is tossed, and it is assumed the chance of getting a head, H, is 1/3 (Thus the chance of getting a tail, T, is 2/3). Consider a random experiment of throwing the coin FIVE times. Let S denote the sample space. Describe the elements of S. (b) (2 pts) Let X be the random variable that corresponds to the number of the heads coming up in 5 times of tossing. What are the values that the random variable X takes?
(C) (2 pts) Find the probability that there is 3 tails and 2 heads, that is, P(X = 2). (d) (2 pts) Find the probability that there are at least 2 heads, that is, P (x > 2)
(e) (2 pts) Suppose that for each toss that coms up heads, we win $4, but for each toss that comes up tails, we lose $3. Clearly, the quantity of interest in this situation is our total winning. Let Y denote this quantity. What re the values the random variable Y can take?