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Unformatted text preview: Problem 5: Suppose we divide the time axis into small periods (0 , t ), ( t, 2 t ), . .. Within each period, we ip a coin independently. The probability of getting a head is t . (1) Let X be the number of heads within the interval [0 ,t ]. Calculate the limit of P ( X = k ) as t 0, for k = 0 , 1 , 2 ,... . Also calculate E[ X ]. (2) Let T be the time until the rst head. Calculate the limit of P ( T > t ) as t 0. In both (1) and (2), let us assume that t is a multiple of t . 1...
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This note was uploaded on 01/29/2010 for the course STATS 100A 262303210 taught by Professor Wu during the Fall '09 term at UCLA.
 Fall '09
 Wu

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