I have got two questions:
Question 1:
Consider a classification task with two classes t1 and t2 with prior probabilities P(t1) = 1/3 and P(t2) = 2/3. Show why the Bayes classifier is not equivalent to the maximum likelihood classifier in that case.
My first idea is that the problem is that the prior probability is not i.i.d. (independent identically distributed).
My second idea is that the Bayes classifier considers the prior probability but the maximum likelihood classifier does not.
Question 2:
Suppose both classes can be modeled with a normal distribution with mean values µ1 = 2 and µ2 = 7 and standard derivation σ1 = σ2 = 1. Use the maximum likelihood classifier to classify the sample x = 5. Make sure to explain all steps.
My idea is to do this by derivate the parameters (µ1, Σ) and finally set the result to zero. But I am also not sure with this.
Thank you very much in advance!