Question

Random variables and expected value

Shared Birthday Height Arrangements Example: How many pairs of people in this room do we expect to share a birthday? Example: If we randomly arrange n people in a line, what is the expected number of people who are taller than all adjacent people? Assume each person's height is different (no ties). If there are 30 people in the room, how many pairs of people are there? What is the probability that two particular people share a birthday? Let X be the number of people who are taller than all adjacent people. What is X for this lineup? Height Arrangements Expectation Does Not Commute Expectation does not in general commute with other functions. Example: If we randomly arrange n people in a line, what is the expected number of people who are taller than all adjacent people? Assume each person's height is different (no ties). E(f(X) ) f(E( # Show how to solve this problem. For example, let X be a random variable with P(X0), P(X-1) Whats E)? What's Ex)? What's (EOX))2

Answer 1

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