I came across this question while practicing EM question but I don't understand how to apply EM in this scenario. What's the latent variable here? Is it the grade of each student? What will be the likelihood function?
Imagine a machine learning class where the probability that a student gets an “A” grade is P (A) = 1/2, a “B” grade P (B) = µ, a “C” grade P (C) = 2µ, and a “D” grade P (D) = 1/2 − 3µ. We are told that c students get a “C” and d students get a “D”. We don’t know how many students got exactly an “A” or exactly a “B”. But we do know that h students got either an a or b. Therefore, a and b are unknown values where a + b = h. Our goal is to use expectation maximization to obtain a maximum likelihood estimate of µ.
Q1) What will be the expected values of a and b given µ?
Q2) Given the expected values of a and b what will be the maximum likelihood estimate of µ?