# Expectation Maximization question

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?

Thanks

• Question might get better replies on stats.stackexchange.com. – cfh Apr 22 '15 at 14:09
• @cfh: how can I move it to stats.stackexchange? Do I need to create a new question there? – alchemist Apr 22 '15 at 14:12
• Click the "flag" link, "in need of moderator intervention", then state that you wish to move it. You can wait a while though if you like, the question isn't off-topic here by any means, maybe there will be answers. – cfh Apr 22 '15 at 14:24