Question: There are n students at a certain school, of whom X ~ Bin(n,p) are Statistics majors. A simple random sample of size m is drawn ("simple random sample" means sampling without replacement, with all subsets of the given size equally likely).
(a) Find the PMF of the number of Statistics majors in the sample, using the law of total probability (don't forget to say what the support is). You can leave your answer as a sum (though with some algebra it can be simpli?ed, by writing the binomial coe?cients in terms of factorials and using the binomial theorem).
(b) Give a story proof derivation of the distribution of the number of Statistics majors in the sample; simplify fully.Hint: Does it matter whether the students declare their majors before or after the random sample is drawn?