Unformatted text preview: T > 5? Problem 3: 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 . (3) Please give a real example of X and T with concrete value of λ and its unit. What is the meaning of λ ? 1...
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 Fall '10
 Wu
 Probability, Meaning of life, STAT 100A HWV

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