Please help me!!
Suppose that r-cylindrical shafts made by machine are selected at random from the production of the machine and their diameters and lengths measured. It is found R11 have both measurements with tolerance limits, R21 have satisfactory diameter but unsatisfactory lengths, and R22 are unsatisfactory as to both measurements.The total sum of Rij is r. Each shaft may be regarded as a drawing from multinomial population with density,
(p11)x11(p12)x12(p21)x21(1-p11-p12-p21)x22 for xij =0,1
having 3 parameters and the sum of all xij is 1. What are the maximum likelihood estimates of the parameters, R11=90, R12 =6,R21 =3, R22 =1?
how am i going to derive the mle for the parameters of multinomial distribution?