Part III

Back to our Maximum Likelihood estimate of r. The general formula is:

L = C + a₁ log m₁ + a₂ log m₂ +...+ a_i log m_i

We take the first derivative of L with respect to r and set this equal to zero to maximize r.

We have shown that m = 1/2(1-r) where we multiply 1/2(1-r) for a single event by n to get the total number expected for n progeny.

Because we substituted m = (1 - r)/2, etc.

n/2 is a constant so when q = a log (1-r)

dq = -  a   because   d log (1-r) = -    1 
dr      1-r  because   d lodr(1-r) = -   1-r