Rao (page 368, 1973) considers a problem in the estimation of linkages in genetics. McLachlan and Krishnan (1997) also discuss this problem and we present their model. For our purposes, it can be described as a multinomial model with the 
where the parameter θ satisfies 0 ≤ θ ≤ 1. In this exercise, we obtain the mle of θ.
(a) Show that likelihood function is given by
(b) Show that the log of the likelihood function can be expressed as a constant (not involving parameters) plus the term
(c) Obtain the partial derivative with respect to θ of the last expression, set the result to 0, and solve for the mle. (This will result in a quadratic equation that has one positive and one negative root.)