Statistics

Use R and paste R code The number of particles emitted by a radioactive source during a ten second interval has the Poisson distribution with mean A. The radioactive source is observed over twenty non-overlapping intervals of ten seconds each. The number of particles emitted during each interval are: 4, 1, 3, 1, 3, 3, 3, 1, 1, 1, 6, 4, 4, 2, 2, 1, 1, 4, 2, 5. a. Using method of moments (show your work) find an estimate for A. b. Create a function to represent your likelihood function from a Poisson distribution and use the sample given above. Plot the function for a range of appropriate possible values of A. Find the value of A that maximized the likelihood. c. Check if the theoretical maximum likelihood estimator for A agrees with the plot from part (b). Explain your results/observations.        

Sample Solution