Suppose that each of two statisticians A and B must estimate a certain parameter p whose value is unknown (0 < p < 1). Statistician A can observe the value of a random variable X, which has the binomial distribution with parameters n = 10 and p; statistician B can observe the value of a random variable Y, which has the negative binomial distribution with parameters r = 4 and p. Suppose that the value observed by statistician A is X = 4 and the value observed by statistician B is Y = 6. Show that the likelihood functions determined by these observed values are proportional, and find the common value of the M.L.E. of p obtained by each statistician.