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Unformatted text preview: (b) Find the expected length of the second run in the binary sequence. Problem 5: (Exercise 21, p. 168) A miner is trapped in a mine containing three doors (possible exits). The frst leads to a tunnel that takes him to saFety aFter two hours oF travel. The second door leads to a tunnel that returns him to the mine aFter fve hours oF travel. The third dooor leads to another tunnel that returns him to the mine aFter three hours. The miner chooses at each time any oF the doors at random. Let N be the total number oF doors selected beFore the miner reaches saFety. Let T i denote the travel time corresponding to the i th choice oF the door ( i ≥ 1). ±inally, let X denote the time until the miner reaches saFety. (a) ±ind an identity that relates X to N and the T i . (b) ±ind EN . (c) ±ind E ( T N ). (d) ±ind E [ ∑ N i =1 T i | N = n ]. (e) Using the preceding, what is EX ?...
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This note was uploaded on 04/15/2010 for the course STAT 416 taught by Professor Denker during the Spring '08 term at Penn State.
- Spring '08
- Stochastic Modeling