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Unformatted text preview: is comprised of dependent random variables. (d) Compute cov( S n , S n +1 ), n = 1 , 2 , . . . . The transition probabilities describe the probability that the process is at a given position at a given time. One quantity of interest is the probability that the SRW is back at the origin at time n ; that is, P { S n = 0 } . Notice that the SRW can only be at the origin after an even number of steps since the only way for it to be at 0 is for there to have been an equal number of steps to the left as to the right. This means it is notationally easier to work with P { S 2 n = 0 } , n = 0 , 1 , 2 , . . . . (e) Determine an expression for P { S 2 n = 0 } , n = 0 , 1 , 2 , . . . . (f) Try and determine an expression for P { S 2 n = x } where  x  2 n has even parity. (That is, x is an even integer between2 n and 2 n .)...
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This note was uploaded on 03/26/2012 for the course STAT 351 taught by Professor Michaelkozdron during the Fall '08 term at University of Regina.
 Fall '08
 MichaelKozdron
 Statistics, Probability

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