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Unformatted text preview: etc.) are modeled well with Poisson random variables. Suppose that for each minute that a Geiger counter is exposed to some source of radiation, the number of beeps N has the Poisson PMF with parameter > 0: p N ( n ) = e n n ! , for n = 0 , 1 , 2 , ... (and zero otherwise) . The numbers of beeps in disjoint minutes are independent. (a) Find the probability of observing 1, 3, 3, and 2 beeps in four disjoint minutes. (That is, the probability of observing 1 beep in the rst minute, 2 beeps in the second minute, and so on.) The answer will depend on . (b) As a way of estimating from the observations in part (a), nd the value of that maximizes the probability found in part (a). This estimate of is called the maximum likelihood estimate. We will return to this topic in Chapter 9. Compiled October 7, 2008 Page 1 of 1...
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 Spring '11
 Proasin
 Computer Science, Electrical Engineering

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