3. A bus runs along a route with stops indexed by n = 1, 2, .......

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3. A bus runs along a route with stops indexed by n = 1, 2, .... Assume that the route is infinitely long and the bus has infinite capacity. The bus arrives empty at Stop 1. When the bus arrives at Stop n, each passenger on it gets off with probability p, independent of each other. Then, a Poisson number of passengers with mean A get on. Assume that the number of passengers getting on at each stop is independent of all other random variables. Let Rn denote the number of passengers on the bus when it leaves Stop n. . Find the distribution of Rn. . As n goes to infinity, what is the limiting distribution of Rn? 3. A bus runs along a route with stops indexed by n = 1, 2, .... Assume that the route is infinitely long and the bus has infinite capacity. The bus arrives empty at Stop 1. When the bus arrives at Stop n, each passenger on it gets off with probability p, independent of each other. Then, a Poisson number of passengers with mean A get on. Assume that the number of passengers getting on at each stop is independent of all other random variables. Let Rn denote the number of passengers on the bus when it leaves Stop n. . Find the distribution of Rn. . As n goes to infinity, what is the limiting distribution of Rn?

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The question states that R n is the number of passengers on the bus when it le... View the full answer