21. Consider Example 3.12 which refers to a miner trapped in a mine. Let N denote the...
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21. Consider Example 3.12 which refers to a miner trapped in a mine. Let N denote the total number of doors selected before the miner reaches safety. Also, let Ti denote the travel time corresponding to the ith choice, i 1. Again let X denote the time when the miner reaches safety.
(a) Give an identity that relates X to N and the Ti.
(b) What is E[N]?
(c) What is E[TN ]?
(d) What is E[
N i=1 Ti|N = n]?
(e) Using the preceding, what is E[X]?
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