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Consider a group of n roommate pairs at a college (so there are 2n students). Each of
Chapter 9, Problem 15(choose chapter or problem)
Consider a group of n roommate pairs at a college (so there are 2n students). Each of these 2n students independently decides randomly whether to take a certain course, with probability p of success (where success is defined as taking the course). Let N be the number of students among these 2n who take the course, and let X be the number of roommate pairs where both roommates in the pair take the course. Find E(X) and E(X|N).
Questions & Answers
QUESTION:
Consider a group of n roommate pairs at a college (so there are 2n students). Each of these 2n students independently decides randomly whether to take a certain course, with probability p of success (where success is defined as taking the course). Let N be the number of students among these 2n who take the course, and let X be the number of roommate pairs where both roommates in the pair take the course. Find E(X) and E(X|N).
ANSWER:Step 1 of 3
Because of the independence between people's choices and the fact that the probability that each pair chooses that course is 
Now it is easy to obtain that
