In this problem, assume that the probability that a person is born on any given day is 1/365. (For simplicity, ignore February 29.) In a group of 100, what is the expected number of sets of two people that have the same birthday? Solve this problem by answering the following questions.

(a) What is the sample space S of this experiment? Hint: we had a related problem in lecture, see the slides. (b) Given two people i and j, define the indicator variable X{ij} by X{ij} = 0 if i and j were born on the same day otherwise What is the expected value E[X{ij}]? (c) Let X be the number of sets of two people that have the same birthday. How does X relate to the variables X{ij} defined above? (d) Use linearity of expectation to find E[X]. Explain where you are using linearity of expectation.