Unformatted text preview: X )? (3) What is the standard deviation of X ? How do you interpret this standard deviation? Problem 3: For X ∼ Geometric( p ), calculate E( X ). Problem 4: Suppose we divide the time axis into small periods (0 , Δ t ), (Δ t, 2Δ t ), . .. Within each period, we ﬂip a coin independently. The probability of getting a head is λ Δ t . (1) Let X be the number of heads within the interval [0 ,t ]. Calculate the limit of P ( X = k ) as Δ t → 0, for k = 0 , 1 , 2 ,... . Also calculate E[ X ]. (2) Let T be the time until the ﬁrst head. Calculate the limit of P ( T > t ) as Δ t → 0. In both (1) and (2), let us assume that t is a multiple of Δ t . 1...
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This note was uploaded on 01/27/2011 for the course STATISTICS 100a taught by Professor Cristou during the Winter '10 term at UCLA.
 Winter '10
 CRISTOU
 Probability

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