+ File | C:/Users/Charlie%20Welch/Downloads/hw6%20(1).pdf m eBay f Facebook YouTube Addons Store 22 Key Macroecono * Studying Tourname... Poker Training - The... (1).pdf 2/2 | - 175% + (b) Find the probability that at least n Route 1 buses will pass by before the first Route bus arrives. The following result from Chapter 7 may be useful here: for independent randon variables X1 ~ Expo()1), X2 ~ Expo(12), we have P(X1 1/(1 + 12). (c) For this part only, assume that /1 = 12 = 1. Find the expected time it will take until both Fred and Gretchen have caught their buses. 5. (BH 5.45) Emails arrive in an inbox according to a Poisson process with rate 20 emails per hour. Let T be the time at which the 3rd email arrives, measured in hours after a certain fixed starting time. Find P(T > 0.1) without using calculus. Hint: Apply the count-time duality. 6. (BH 6.19) Use MGFs to determine whether X + 2Y is Poisson if X and Y are i.i.d. Pois()). 7. (BH 6.22) Consider a setting where a Poisson approximation should work well: let Al, ..., An be independent. rare events. with n large and p; = P(A;) small for all 7. Let X = I(A, ) + se hero.html Show all Type here to search O Eli B 480F ~ ( 2 () ENG 9:29 PM US 10/27/2021 ALIENWARE