4. (worth 15 points) A biased coin with P(heads)-.65 is flipped 8 times. Let X be the random variable of the number of heads observed. a. What distribution best fits this scenario? (circle one answer below) i. Binomial ii. Negative Binomial iii. Poisson b. What are all of possible values that X can take? c. What is the probability that heads is observed exactly 4 times out of the 8 flips i.e. P(X 4)? (worth 20 points) The Los Angeles Dodgers are facing the Milwaukee Brewers in the first round of the playoff series. Suppose it is assumed that the probability that the Dodgers will beat the Brewers in any single game is 0.6. A team wins the playoff series if it wins 3 out of 5 games. 5. What is the probability that the Dodgers win the series in 4 games? What is the probability that the Dodgers will win the series? What is the probability that Brewers will win the series in 5 games? a. b. c. What is the expected number of games that the Dodgers will play in order to win the series? (i.e., what is E[X] where X is number of games Dodgers play to win the playoff series?) d