In this problem, assume that the probability that a person is born on a given day is 1/365. (For simplicity, ignore Feb 29.) In a group of 100, what is the expected number of pairs of people who 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 Xij) by if i and j were born on the same day 1 Xi0 otherwise is the expected value EX What X relate to the variables Xfij) defined above? expectation (c) Let X be the number of sets of two people that have the same birthday. How does X relate to the variables X{i, j} defined above?(d) Use linearity of expectation to find E[X]. Explain where you are using linearity of expectation