1. For a binary symmetric channel, the error probability Pc(0) = Pc(1) = and errors are statistically independent. The channel capacity for a signalling speed 2 bits/second.





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MCQ->For a binary symmetric channel, the error probability Pc(0) = Pc(1) = and errors are statistically independent. The channel capacity for a signalling speed 2 bits/second.....
MCQ-> Analyze the following passage and provide appreciate answers for the questions that follow. Ideas involving the theory probability play a decisive part in modern physics. Yet we will still lack a satisfactory, consistence definition of probability; or, what amounts to much the same, we still lack a satisfactory axiomatic system for the calculus of probability. The relations between probability and experience are also still in need of clarification. In investigating this problem we shall discover what will at first seem an almost insuperable objection to my methodological views. For although probability statements play such a vitally important role in empirical science, they turn out to be in principle impervious to strict falsification. Yet this very stumbling block will become a touchstone upon which to test my theory, in order to find out what it is worth. Thus, we are confronted with two tasks. The first is to provide new foundations for the calculus of probability. This I shall try to do by developing the theory of probability as a frequency theory, along the lines followed by Richard von Mises, But without the use of what he calls the ‘axiom of convergence’ (or ‘limit axiom’) and with a somewhat weakened ‘axiom of randomness’ The second task is to elucidate the relations between probability and experience. This means solving what I call the problem of decidability statements. My hope is that the investigations will help to relieve the present unsatisfactory situation in which physicists make much use of probabilities without being able to say, consistently, what they mean by ‘probability’.The statement, “The relations between probability and experience are still in need of clarification” implies that:
 ....
MCQ-> People are continually enticed by such "hot" performance, even if it lasts for brief periods. Because of this susceptibility, brokers or analysts who have had one or two stocks move up sharply, or technicians who call one turn correctly, are believed to have established a credible record and can readily find market followings. Likewise, an advisory service that is right for a brief time can beat its drums loudly. Elaine Garzarelli gained near immortality when she purportedly "called" the 1987 crash. Although, as the market strategist for Shearson Lehman, her forecast was never published in a research report, nor indeed communicated to its clients, she still received widespread recognition and publicity for this call, which was made in a short TV interview on CNBC. Still, her remark on CNBC that the Dow could drop sharply from its then 5300 level rocked an already nervous market on July 23, 1996. 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The smaller the sample used, however (or the shorter the record), the more likely the findings are chance rather than meaningful. Yet the Tversky and Kahneman study showed that typical psychological or educational experimenters gamble their research theories on samples so small that the results have a very high probability of being chance. This is the same as gambling on the single good call of an advisor. The psychologists and educators are far too confident in the significance of results based on a few observations or a short period of time, even though they are trained in statistical techniques and are aware of the dangers.Note how readily people over generalize the meaning of a small number of supporting facts. Limited statistical evidence seems to satisfy our intuition no matter how inadequate the depiction of reality. Sometimes the evidence we accept runs to the absurd. A good example of the major overemphasis on small numbers is the almost blind faith investors place in governmental economic releases on employment, industrial production, the consumer price index, the money supply, the leading economic indicators, etc. These statistics frequently trigger major stock- and bond-market reactions, particularly if the news is bad. Flash statistics, more times than not, are near worthless. Initial economic and Fed figures are revised significantly for weeks or months after their release, as new and "better" information flows in. Thus, an increase in the money supply can turn into a decrease, or a large drop in the leading indicators can change to a moderate increase. These revisions occur with such regularity you would think that investors, particularly pros, would treat them with the skepticism they deserve. Alas, the real world refuses to follow the textbooks. 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Governmental economic releases on macroeconomic indicators fetch blind faith from investors who appropriately discount these announcements which are ideally reflected in the stock and bond market prices. III. Investors take into consideration myopic gain and make it meaningful investment choice and fail to see it as a chance of occurrence. IV. lrrational overreaction to key regulators expressions is same as intuitive statistician stumbling disastrously when unable to sustain spectacular performance.....
MCQ->Consider a Binary Symmetric Channel (BSC) with probability of error being p. To transmit a bit, say 1, we transmit a sequence of three 1 s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is....
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