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Tham khảo tài liệu 'introduction to communication systems, the theory of probability', kỹ thuật - công nghệ, tự động hoá phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Introduction to Communication Systems The Theory of Probability Probability Theory Why Probability Probability theory is applied to situations where uncertainty exists. These situations include 1. The characterization of traffic at the intersection US 460 and Peppers Ferry Road i.e. the number of cars that cross the intersection as a function of time 2. The prediction of the weather in Blacksburg 3. The number of students traversing the Drill Field between 8 50 and 9 00 on Mondays 4. The thermally induced Brownian motion of molecules in a a copper wire b a JFET amplifier Note that the latter two situations would resort in a phenomenon known as noise whose power would be a function of the Temperature of the molecules. In all of these situations we could develop an excellent approximation or prediction for each of these experiments. However we would never be able to characterize them with absolute certainty i.e. deterministically . However we could characterize them in a probabilistic fashion or probabilistically via the elements of probability theory. This is what weather forecasters are doing when they say The chance of rain tomorrow is 40 In such cases they are saying that the probability of a rain even is 0.4. Other probabilistic characterizations include One the average 300 cars per minute cross US 460 and Peppers Ferry Road at Noon on Saturdays. The chances of so many cars crossing that intersection at 8 00 AM on Sunday is very small The average noise power produced by this amplifier is 1 zIU Scientists and Engineers apply the theories of Probability and Random Processes to those repeating situations in nature where 1. We can roughly predict what may happen. 2. We cannot exactly determine what may happen Whenever we cannot exactly predict an occurrence we say that such an occurrences is random. Random occurrences occur for the following reasons All the causal forces at work are unknown. Insufficient data for the conditions of the problem do not exist The .
