In: Advanced Math
Suppose X1, X2, ..., Xn iid∼ Multinomial (p). a) What is the MLE for the situation where p = (p1, p2, p3, p4), such that p1 = p2 and p3 = p4? b) What can you interpret from these estimates in terms of the number of observations of type k (k = 1, 2, 3, 4) compared the total number of trials n?
Answer:-
Given that
p = ( p1,p2,p3,p4) than p1 =p2 , p3=p4
Suppose X1, X2, ..., Xn iid∼ Multinomial .
let the goal of maximum likelihood is to find the parameter values that give the distribution that maximise the probability of observing the data