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.

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(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. (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.