Suppose that each of two statisticians A and B must estimate a certain parameter 0 whose value is unknown (0 > 0). Statistician A can observe the value of a random variable X which has a gamma distribution with parameters a and /3, where €X = 3 and {3 = 8; and statistician B can observe the value of a random variable Y which has a Poisson distribution with mean 20. 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 0 obtained by each satisfaction.