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Let a four-letter alphabet have probabilities p = [0.7, 0.1, 0.1, 0.1] 5.22 a. What is...
Q2) Design a Huffman code for a 2-letter alphabet with probabilities. Compute the entropy of that source. Design a Huffman code for the second third and fourth extensions of the source. Compute the average code word length for each extension.
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
Let x be an exponential random variable with 1 = 0.7. Calculate the probabilities described below. a. Plx < 4) P(x<4) = (Round to four decimal places as needed.) b. P(x > 8) P(x > 8) = 0.0017 (Round to four decimal places as needed.) c. P(4 SX 58) P(4 x 8) = (Round to four decimal places as needed.) d. Plx 3) P(x 3) = (Round to four decimal places as needed.) e. the probability that x is at...
Let y-and Г be two alphabets, and let Г be the alphabet be the alphabet of vectors where the first element is from Σ and the second is from「 For example, if -(a,b) and Г-{0.1} then and B c Г be any regular languages, and consider the language Let A Show A B is regular.
Let y-and Г be two alphabets, and let Г be the alphabet be the alphabet of vectors where the first element is from Σ and...
9) Let.4, B and Cbe independent events with P(A)-0.1, P(B) 0.7, and P(C) 0.9. Find P(A and B and C). A) 0.078 B) 0.037 C) 0.063 D) 0.07
Let x be an exponential random variable with λ = 0.7. Calculate the probabilities described below. a. P(x < 4) P(x < 4) = ______ . (Round to four decimal places as needed.) b. P(x > 8) P(x > 8) = ______ . (Round to four decimal places as needed.) c. P(4 ≤ x ≤ 8) P(4 ≤ x ≤ 8) = ______ . (Round to four decimal places as needed.) d. P(x ≥ 3) P(x ≥ 3) = ______...
Let x be an exponential random variable with λ = 0.7. Calculate the probabilities described below. a. P(x < 4) P(x < 4) = ______. (Round to four decimal places as needed.) b. P(x > 8) P(x > 8) = ______ . (Round to four decimal places as needed.) c. P(4 ≤ x ≤ 8) P(4 ≤ x ≤ 8) = ______ . (Round to four decimal places as needed.) d. P(x ≥ 3) P(x ≥ 3) = ______ ....
Let X be a binomial random variable with p four decimal places (e.g. 98.7654) 0.7 and n 10. Calculate the following probabilities from the binomial probability mass function. Round your answers to Px-40.0352 P3 X 5)- 0.0435 Statistical Tables and Chart
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3. State and explain channel capacity theorem. (4 marks) a) b) The probabilities of occurrence of various letters of the English alphabet are given below: A 0.091, M 0.001, P = 0.040, X= 0.001 What letter(s) convey(s) the maximum amount of information? Compute this information content (6 marks) c) An information source is to transmit the message MALAYSIA" repeatedly. What are the codewords needed at the decoder when the message is...
(h) What is P(AB) if P(AB) - 0.1? (2 pts) () What is P(AB) if P(AB) - 0.7? (3 pts) (2) A certain disease is prevalent in 10% of a given population. Scientists have developed a test for the disease. In the laboratory, the test correctly identifies samples known to have the disease 98% of he time. Also, the test is positive incorrectly 7% of the time when testing samples known not to have e disease. A doctor uses this...