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 λ > 0: p N ( n ) = eλ λ 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 λ . (b) As a way of estimating λ from the observations in part (a), ±nd the value of λ that maximizes the probability found in part (a). This estimate of λ 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, Probability, Probability theory, Department of Electrical Engineering & Computer Science

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