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Suppose that each of two statisticians A and B must estimate a certain parameter theta whose value is unknown (theta > 0). Statistician A can observe the value of a random variable X which has a gamma distribution with parameters alpha and beta, where alpha = 3 and beta = theta; and statistician B can observe the value of a random variable Y which has a Poisson distribution with mean 2(theta). Suppose that the value observed by statistician A is X = 2 and the value observed by statistician B is Y = 3. Show that the likelihood functions determined by these observed values are proportional, and find the common value of the M.L.E. of theta obtained by each statistician. The M.L.E. is closest to:
  • 2/3
  • 1/6
  • 3/2
  • 2
  • 3
  • *****
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    Carlos Rodriguez <carlos@math.albany.edu>
    This problem was contributed by a student. It is offered as it is with no warranty of any kind
    Last modified: Wed May 13 12:29:11 EDT 1998