5.9 Check, using both direct optimisation and the EM algorithm, that = 0.627 in the multinomial model with data: [125 18 20 34] and

5.9 Check, using both direct optimisation and the EM algorithm, that μ =

0.627 in the multinomial model with data: [125 18 20 34] and cell probabilities 1 1 2 + π

4 , 1 4 (1 − π), 1 4 (1 − π), π

4 2

.

Obtain the quadratic equation satisfied by the maximum-likelihood estimate π. As an exercise in using the fzero command in Matlab use fzero to check the value for π.