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Suppose that a following board is sliced up into regions as shown in the image below. First its cut into two, then one of the resulting small regions is again divided in half, and so on. This happens for N stages, then the division processed is stopped, and subsequently a dart is thrown. Now if there is O information known about the dart, except the fact that the probability per unit area is equivalent for it to strike anywhere on the given circle, please solve for how many bits of info are missing concerning what region it landed in. What happens in the limit N → 0? [Hint: CAo ræ" = r4ENor".]

Suppose that a following board is sliced up into regions as shown in the image below. First its cut into two, then one of the resulting small regions is again divided in half, and so on. This happens for N stages, then the division processed is stopped, and subsequently a dart is thrown. Now if there is O information known about the dart, except the fact that the probability per unit area is equivalent for it to strike anywhere on the given circle, please solve for how many bits of info are missing concerning what region it landed in. What happens in the limit N → 0? [Hint: CAo ræ" = r4ENor".]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that a following board is sliced up into regions as shown in the image below. First its cut into two, then one of the resulting small regions is again divided in half, and so on. This happens for N stages, then the division processed is stopped, and subsequently a dart is thrown. Now if there is O information known about the dart, except the fact that the probability per unit area is equivalent for it to strike anywhere on the given circle, please solve for how many bits of info are missing concerning what region it landed in. What happens in the limit N → x? [Hint: Era" = rEo r".) Diagram for this problem:
Transcribed Image Text:Suppose that a following board is sliced up into regions as shown in the image below. First its cut into two, then one of the resulting small regions is again divided in half, and so on. This happens for N stages, then the division processed is stopped, and subsequently a dart is thrown. Now if there is O information known about the dart, except the fact that the probability per unit area is equivalent for it to strike anywhere on the given circle, please solve for how many bits of info are missing concerning what region it landed in. What happens in the limit N → x? [Hint: Era" = rEo r".) Diagram for this problem:
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