4. There is a 25% chance that Tony Stark will talk about being a billionaire in any given sentence. Assume that this probability is fixed and independent between sentences. (a) (2 points) What is the probability that Tony talks about being a billionaire for the first time in his 5th sentence? (b) (3 points} What is the probability that the 4th time Tony mentions that he is a billionaire occurs on the 20th sentence ? 5. Lil Jon gives free Coronavirus shots according to a Poisson Process with rate A = 10 per hour. Let X be a random variable representing the number of shots given between 2:00pm and 4:30pm. (a) (2 points ) What is the distribution of X? (b) (3 points) What is the probability that exactly 24 shots are given between 2:00pm and 3:30pm ? (c) (2 points } What is the variance of the number of shots given between 4:00pm and 5:00pm '? (d) (3 points } What is the probability that at least one shot is given in any one minute interval