Sta3007_Ass2 - STA 3007 Assigment 2 Due date 26 th October...

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Unformatted text preview: STA 3007 Assigment 2 Due date: 26 th October, 2005 1. You have five fair coins. You toss them all so that they randomly fall heads or tails. Those that fall tails in first you pick up and toss again. You toss again those which show tails after the second toss, and so on, until all show heads. Let X be the number of coins involoved in the last toss. Find Pr { X = 1 } . 2. A bus in a mass transit system is operating on a continuous route with intermediate stops. The arrival of the bus at a stop is classified into one of three states, namely (a) Early arrival: (b) On-time arrival; (c) Late arrival. Suppose that the successive states form a Markov chain with transition probability matrix 1 2 3 P = 1 2 3 vextenddouble vextenddouble vextenddouble vextenddouble vextenddouble vextenddouble . 5 . 4 . 1 . 2 . 5 . 3 . 1 . 2 . 7 vextenddouble vextenddouble vextenddouble vextenddouble vextenddouble vextenddouble Over a long period of time, what fraction of stops can be expected to be late?...
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