Question: A random variable can take on any of possible values x 1 , ... , x n with respective probabilities p(x i ), i =

A random variable can take on any of possible values x₁, ... , x_n with respective probabilities p(x_i), i = 1, ..., n. We shall attempt to determine the value of by asking a series of questions, each of which can be answered “yes” or “no.” For instance, we may ask “Is X = x₁?” or “Is X equal to either x₁ or x₂ or x₃?” and so on. What can you say about the average number of such questions that you will need to ask to determine the value of X?

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