4. A telescope pointed at a region of space observes 0.01 shooting starsfday on average. Assume shooting stars are independent events- a) Even though it's arguably not the best t, suppose we choose to use a binomial random variable to model the number of shooting stars observed in a 365day year, setting in = 365 and p = 0.01. Determine the mean, the standard deviation, and the maximum outcome theoretically possible for this model (but not this maximum's probability). You may use 'shortcut formulas' that apply to this probability distribution. b) Suppose we instead choose to use a Poisson random variable to model the number of shooting stars observed in a 365day year. Determine the appropriate param eter value, the mean, and the standard deviation for this random variable. You may use 'shortcut formulas' that apply to this probability distribution. c) Describe an outcome value that is (theoretically) possible with the Poisson model used in part b) but not possible with the Binomial model used in part a). What (very) improbable sequence of events would need to happen on at least one day in order for this Poissonspecic outcome to occur? d) A commonly used \" rule of thumb\" dictates that 95% of outcomes should occur within two standard deviations of the mean. Using the means and standard deviations you calculated in parts a) and b), use this rule of thumb to construct intervals that contain 95% of outcomes for each of these random variables. Are these intervals similar? (The lower boundaries for the intervals might seem a bit peculiar. Don't worryr about it!)