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Please provide clear explanation and show your steps. Thank you! 7. Friends (10 points) Consider a group of n people where each pair of people

Please provide clear explanation and show your steps. Thank you!

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7. Friends (10 points) Consider a group of n people where each pair of people is friends independently with probability 1/2. What is the expected number of triples of pe0p|e that are all friends, i.e. triples AB, C such that A is friends with B and B is friends with C and A is friends with C. Use linearity of expectation and carefully define indicator random variables (0/1 valued random variables) and justify your work

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