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5. (Data from Poisson process) A detector counts the number of particles emitted froma radioactive source over the course of lD-second intervals. For 180 such lO—secondintervals, the following counts were observed: Count # intervals0 23773426137 th-WMI—l This table states, for example, that in 34 of the lO-second intervals a count of 2 wasrecorded. Sometimes, however, the detector did not function properly and recordedcounts over intervals of length 20 seconds. This happened 20 times and the recordedcounts are Count # intervals0 2 l 42 93 5 Assume a Poisson process model for the particle emission process. Let A > 0 (timeunit = 1 sec.) be the unknown rate of the Poisson process. (a) Formulate an appropriate likelihood function for the described scenario andderive the maximum likelihood estimator A of the rate A. Compute A for theabove data. (b) What approximation to the distribution of ; does the central limit theoremsuggest? (Note that the sum of all 200 counts has a Poisson distribution. Whatis its parameter?)
