1. Math
  2. Statistics And Probability
  3. please only answer part b the solution to a...

Question: please only answer part b the solution to a...

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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 folowig counts were observed: Count # intervals 23 34 26 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 f length 20 seconds. This happened 20 times and the recorded counts are Count # intervals 9 Assume a Poisson process model for the particle emission process. Let λ > 0 (time 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 (b) What approximation to the distribution of A does the central limit theorem suggest? (Note that the sum of all 200 counts has a Poisson distribution. What is its parameter?)

PLEASE ONLY ANSWER PART B - THE SOLUTION TO A SHOULD BE THE WEIGHTED AVERAGE OF EVENTS, THAT IS XBAR

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