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###### Part 3 7. A detector counts the number of particles emitted from a radioactive source over...

Part 3 7. A detector counts the number of particles emitted from a radioactive source over the course of 10-second intervals. For 180 such 10-second intervals, the following counts were observed: Count # intervals 34 3 13 This table states, for example, that in 34 of the 10-second intervals a count of 2 was recorded. Sometimes, however, the detector did not function properly and recorded counts over intervals of length 20 seconds. This happened 20 times and the recorded counts are Count # intervals 2 3 9 Assume a Poisson process model for the particle emission process, let λ > 0 (tine unit 1 sec.) be the unknown rate of the Poisson process. (a) Formulate an appropriate likelihood function for the described scenario and derive the maximum likelihood estimator λ of the rate λ. Compute λ for the above data.

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