I understand for a random variable to be distributed binomially:
- There must be n fixed trials
- Each trial must be independent of the others
- Probability of success must remain constant throughout the trials
- Outcome either happens or doesn't happen
So take this set up (sorry for the big chunk of text):
A university scholarship committee must select two students to receive a certain scholarship. The committee receives eight applications for the scholarships - five from male students and three from female students. The applicants are all equally qualified, so the two scholarship winners are randomly selected from the eight applicants. Let X be the number of female students who receive a scholarship.
From what I understand, X is indeed a binomial random variable but this is where my confusion arises.
Is X ~ Bin(3,3/8) or X ~ (8,3/8)?
I wasn't sure if n refers to all 8 possible students or just the 3 female students.