Home Assignment #1 Solutions
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چکیده
For a fair coin p = 12 . Therefore, H(X) = 2. (b) We need for each question to reduce our uncertainty about X as much as possible. To do this, we should ask questions which are equally likely to receive a yes or no answer. Before we start asking questions, X = 1 is just as likely as X > 1 (since p = 12 for a fair coin); all other specific values X = 1, 2, . . . are less likely. So the first question should be X = 1?. If the answer is ‘yes,’ we’re done. If ‘no’, then we are essentially back to the original situation: the next flip is equally likely to be heads or tails, so P (X = 2) = P (X > 2) and the second question should be X = 2? (of course, asking X > 2? will get us the same information). So a good sequence of questions seems to be:
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تاریخ انتشار 2003