(a) A two-state Markov process may emit '0' in State 0 or emit '1' in State...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(a) A two-state Markov process may emit '0' in State 0 or emit '1' in State 1, each with probability a, and return to the same state; or with probability 1 - a it emits the other symbol and switches to the other state. Thus it tends to be "sticky" or oscillatory, two forms of predictability, depending on a. '0' 1. What are the state occupancy probabilities for 0 < a <1? Two-State Markov Process State 0 p=1-a '0' '1' p=1-a State 1 '1' 2. What are the entropy of State 0, the entropy of State 1, and the overall entropy of this source? Express your answers in terms of a. 3. For what value(s) of a do both forms of predictability disappear? What then is the entropy of this source, in bits per emitted bit? (b) Consider an alphabet of 8 symbols whose probabilities are as follows: ABCDE|F|G|H 128 1. If someone has selected one of these symbols and you need to discover which symbol it is by asking 'yes/no questions that will be truthfully answered, what would be the most efficient sequence of such questions that you could ask in order to discover the selected symbol? 2. By what principle can you claim that each of your proposed questions is maximally informative? 3. On average, how many such questions will need to be asked before the selected symbol is discovered? (c) Huffman trees enable construction of uniquely decodable prefix codes with optimal codeword lengths. The five codewords shown here for the alphabet {A,B,C,D,E} form an instantaneous prefix code. 1. Give a probability distribution for the five letters that would result in such a tree; 2. Calculate the entropy of that distribution; 3. Compute the average codeword length for encoding this alphabet. Relate your results to the Source Coding Theorem. A 00 ? B 01 C 10 D 110 E 111 (a) A two-state Markov process may emit '0' in State 0 or emit '1' in State 1, each with probability a, and return to the same state; or with probability 1 - a it emits the other symbol and switches to the other state. Thus it tends to be "sticky" or oscillatory, two forms of predictability, depending on a. '0' 1. What are the state occupancy probabilities for 0 < a <1? Two-State Markov Process State 0 p=1-a '0' '1' p=1-a State 1 '1' 2. What are the entropy of State 0, the entropy of State 1, and the overall entropy of this source? Express your answers in terms of a. 3. For what value(s) of a do both forms of predictability disappear? What then is the entropy of this source, in bits per emitted bit? (b) Consider an alphabet of 8 symbols whose probabilities are as follows: ABCDE|F|G|H 128 1. If someone has selected one of these symbols and you need to discover which symbol it is by asking 'yes/no questions that will be truthfully answered, what would be the most efficient sequence of such questions that you could ask in order to discover the selected symbol? 2. By what principle can you claim that each of your proposed questions is maximally informative? 3. On average, how many such questions will need to be asked before the selected symbol is discovered? (c) Huffman trees enable construction of uniquely decodable prefix codes with optimal codeword lengths. The five codewords shown here for the alphabet {A,B,C,D,E} form an instantaneous prefix code. 1. Give a probability distribution for the five letters that would result in such a tree; 2. Calculate the entropy of that distribution; 3. Compute the average codeword length for encoding this alphabet. Relate your results to the Source Coding Theorem. A 00 ? B 01 C 10 D 110 E 111
Expert Answer:
Related Book For
Management Accounting Information for Decision-Making and Strategy Execution
ISBN: 978-0137024971
6th Edition
Authors: Anthony A. Atkinson, Robert S. Kaplan, Ella Mae Matsumura, S. Mark Young
Posted Date:
Students also viewed these programming questions
-
Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...
-
ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...
-
a. Given the following information, calculate the expected value for Firm Cs EPS. Data for Firms A and B are as follows: E(EPS A ) = $5.10, and A = $3.61; E(EPS B ) = $4.20, and B = $2.96. b. You...
-
For the designs found in part (a) of Problem 22, evaluate the steady-state error due to a unit-ramp command and due to a unit-ramp disturbance. In Problem 22 (a) Compute the required gain values for...
-
Simplify. -2v 3 3 4 Write your answer without parentheses.
-
Which one of the following does not relate to diesel engines ? (a) fuel pump (b) fuel injector (c) governor (d) carburettor
-
The adjusted trial balance of Hanlon Corporation at December 31, 2012, includes the following accounts: Retained Earnings $17,200; Dividends $6,000; Service Revenue $32,000; Salaries and Wages...
-
Would a transformational leader make a more successful strategic leader? Why should a transformational leader be better suited to do, as they work toward that common goal of inspiring individuals of...
-
Discuss the impact of organizational trust and how it can resolves the issues within an organization?
-
How do organizational culture and leadership style impact the formulation and execution of strategy, and how can leaders cultivate a strategic mindset and foster alignment throughout the organization...
-
what ways can organizations leverage strategic alliances, mergers, and acquisitions as part of their growth and diversification strategies, while mitigating risks and ensuring synergistic value...
-
Write a function ref_triangular which uses reflections to turn an m X n matrix M into an upper triangular matrix. The output should be a list [Q,R] where is a product of reflections and R is upper...
-
How do organizations effectively balance emergent strategies with deliberate strategies in dynamic environments characterized by uncertainty and rapid change ?
-
Refer to the graph and answer the following questions: Output Time A a. Line A is the typical trend in [(Click to select) b. Line B is the typical trend in (Click to select) B
-
Describe its content and suggest a meaning in a report. Nightmare the painting by henry Fuseli called the nightmare made in 1781 from oil and canvas. in this painting i see a women lying on a bed and...
-
In exchange for land, the company received a 12-month note on January 1. The face amount of the note is $1,000, and the stated rate of interest is 13%, compounded annually. The 13% rate is equal to...
-
A university is deciding between two meal plans. One plan charges a fixed fee of \($600\) per semester and allows students to eat as much as they want. The other plan charges a fee based on the...
-
Evaluate this statement: You are a natural athlete, an attractive person who learns easily and communicates well. Clearly, you can do everything better than your friends and acquaintances. As a...
-
In elementary school and through middle school, most students have the same teacher throughout the day and for the entire school year. Then, beginning in high school, different subjects are taught by...
Study smarter with the SolutionInn App