16. A random variable can take on any of n possible values x, x, with respective probabilities...

16. A random variable can take on any of n possible values x₁, x, with respective probabilities p(x₁), i = 1,...,n. We shall attempt to determine the value of X by asking a series of questions, each of which can be answered by "yes" or "no." For instance, we may ask "Is Xx₁?" or "Is X equal to either x, 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?