Consider a genetics problem in which each individual in a certain population must have one of six

Question:

Consider a genetics problem in which each individual in a certain population must have one of six genotypes, and it is desired to test the null hypothesis H0 that the probabilities of the six genotypes can be represented in the form specified in Eq. (10.2.2).
a. Suppose that in a random sample of n individuals, the observed numbers of individuals having the six genotypes are N1, . . . , N6. Find the M.L.E.’s of θ1 and θ2 when the null hypothesis H0 is true.
b. Suppose that in a random sample of 150 individuals, the observed numbers are as follows:
N1 = 2, N2 = 36, N3 = 14, N4 = 36,
N5 = 20, N6 = 42.
Determine the value of Q and the corresponding tail area.