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Unformatted text preview: 1,4], and let Y = X 1 (a) Find E[ Y ]. (b) Find f Y (v), the probability density function of Y . 4. Consider a Poisson process with arrival rate 2 per second. Let A denote the event that there are no arrivals in the time interval (0, T] and B the event that there is exactly one arrival in the time interval (0.5T, 1.5T]. (a) What are the values of P(A) and P(B)? (b) Find P(B  A). 5. A coin is tossed once, and heads shows. Assuming that the probability p of heads is the value of a random variable X uniformly distributed in the interval (0.4,0.6), find the probability that at the next tossing heads will show. ( Hint: The asked probability is the Bayesian estimate of probability of heads after the observation)....
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 Spring '09
 NegarKayavash

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