How do I find the mle for r1 and r2 if:
p(x1,x2) = 1 - r1^x1 * r2^x2 ,
r1 <1, r2 < 1
given that x1 and x2 can be either 1 or 0 (i.e. it can be either (0,0), (0,1), (1,1) or (1,0) ?
Any help will be appreciated.
Here is the full explanation:
There are two risk factors that may cause an accident to happen. A risk factor is either present (x = 1) or absent (x = 0).
We have a function that specifies probability p(x1, x2) of an accident, but not the outcome in every concrete case.
We assume that each risk factor reduces the probability of a good outcome (no accident) by some factor . In other words, the unknown function
p is of the form , so we have to learn parameters .
How would you compute the ML hypothesis from the data, under the given assumption on p?