Question

Ex 1. Assume that birthdays of people in general are equally distributed among the 12
months. We consider a class of n students.
i) What is the probability that a student has his/her birthday in a given month?
ii) What is the probability that k students have their birthday in a given month?
For each month (labelled by i) we dene a discrete random variable Xi
, such that
Xi =
(
1 if the ith month has birthdays of exactly k students
0 otherwise
iii) What is the expectation value of Xi
iv) What is the expected number of months that have birthdays of exactly k students?