Consider a trinary communication channel [STAR 1979] whose channel diagramis shown in Figure 1.P.6. For i = 1,2, 3 let T; denote the event "digit i is trans-mitted" and let R, denote the event “digit i is received." Assume that a 3 istransmitted 3 times more frequently than a 1, and a 2 is sent twice as often as 1.If a 1 has been received, what is the expression for the probability that a1 wassent? Derive an expression for the probability of a transmission error.P(R1IT1) =1-T1R1a / 2a / 2B/21-BT2R2B/2y/2y/21-yT3R3Figure 1.P.6. A trinary communication channel: channel diagram

Answered: Image /qna-images/answer/9494a740-ae42-4b2f-9396-817e3f9272ee.jpg

Answered: Consider a trinary communication…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

8.) Six letters of the alphabet are chosen at random. Find the probability that the following "words" are formed: (a) REDSOX (b) A "word" that ends in Y (c) A "word" with no repeated letters (d) A "word" that does not contain A,B, or C
3) An engineer has developed a prototype for a new device which contains multiple components. The probability that component A does not fail is .95, the probability that component B does fail is .13, and the probability that both components do not fail is .84. Include the probability statements in terms of event A(component A does not fail) and event B(component B does not fail), using the symbols U and n. a) What is the probability at least one component fails? b) What is the probability exactly one component fails? c) What is the probability that both components fail? d) What is the probability that component A fails or that component B does not fail?
In a Binary Symmetric (Communication) Channel (BSC) data is sent data is sent using bits 0 and 1. Whenthe source and the destination are far apart, there are repeaters that decode the bit and transmit generate asignal. However due to noise, there decoding error, i.e., there a probability α that a bit 0 will be decodedas (and hence transmitted) as 1. Similarly, β is the probability that a bit 1 will be decoded as (and hencetransmitted as) 1. Let X0 be the bit’s initial parity and and let Xn be the bits parity after the nth repeater.1. Construct the one-step transition matrix for this Markov Chain.2. Suppose the input stream to this communication channel consists of 80% 0s and 20% 1s. Determinethe proportion of 0s and 1s after the first repeater.3. Under the same input values as in (b) determine the proportions of 0s and 1s exiting the 5th relay.
In a soon to be released Halloween martial arts movie, a pumpkin has a starring role. Because of the rather violent nature of the film, the producers have also hired a stunt pumpkin. Suppose the featured pumpkin appears in 40% of all the film scenes, the stunt pumpkin appears in 30% of the film scenes and the two appear simultaneously in 5% of the scenes. Draw the Venn diagram to reflect information given in the problem. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene mutually exclusive (disjoint)? Explain how you know. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene independent? Explain how you know. What is the probability that in a given scene that only the stunt pumpkin appears? You have three events A, B, & C. Suppose: Event A is the event of drawing a king from a deck of 52 cards on the first draw. Event B is the probability of drawing a queen of hearts on the…
3. 01:26:35 The following two-way table shows the distribution of daily traffic and weather issues in a certain large city. Suppose a day from this city is selected at random. Let event A = heavy traffic and event B = bad weather. Are events A and B independent? Daily Traffic No, P(A) = P(B|A). Нeavy Traffic Light Traffic Total O No, P(A) + P(A|B). O Yes, P(A) = P(A|B). O Yes, P(A) + P(B|A). Bad Weather 25 30 Good Weather 55 15 75 Total 80 20 100 Weather Conditions
6. A smoke detector system uses two devices, an ionization sensor and a photoelectric sensor. If smoke is present, the probability that it will be detected by the ionization sensor (I) is 0.90, by the photoelectric sensor (P), 0.80, and by both devices, 0.72. a) Draw a Venn diagram to represent the problem. b) If smoke is present, determine the probability that the smoke will be detected by the system. c) if smoke is present, determine the probability that the smoke is undetected. d) are the two alarms operating independently. Justify your answer with a calculation.
A person, Joe, claims to be able to "smell" an illness based on the odor of a person's clothing. Joe is given 12 shirts, each worn by a different person, some of whom had the illness and some of whom did not. The shirts were given to Joe in random order and he had to decide whether each shirt had been worn by an ill patient or by a healthy patient. joe identified 11 of the 12 shirts correctly. If we assume that Joe was just guessing, he would have probability 1/2 of correctly identifying each shirt. Find the probability that Joe would identify AT LEAST 11 shirts correctly by random guessing
1. Four people are seated around a table as in the diagram below. Another clumsy person accidentally spills water on two adjacent people at the table. (For example, the water could be spilled on 1 and 2, or on 1 and 4, but not on 1 and 3.) The clumsy person is equally likely to spill water on any of the four adjacent pairs. 2 Let W₁ be the event "person 1 had water spilled on them". Define W2, W3, W4 similarly. (a) Which pairs of the events W₁, W2, W3, W₁ are independent? Explain why. (b) Which pairs of the events W₁, W2, W3, W4 are disjoint? Explain why.
section 5.3 Out of 413 applicants for a job, 127 have over 10 years of experience and 51 have over 10 years of experience and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience? Enter a fraction or round your answer to 4 decimal places, if necessary. Step 2 of 2: Consider that 83 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 10 yrs of experience, given that the applicant has a graduate degree? round to 4 decimal places
A circuit has three independent switches A, B , C wired inparallel. current can only flow through the bank of switches if at least one of them is closed. The probability that any given switch is closed is 0.9. calculate the probability that the current can flow throught the bank of switches.
A card is randomly drawn from a deck of well-shuffled playing cards. Let event E be that the card is a king and event F be that the card is a diamond. A standard 52-card deck is split evenly into four suits of cards (hearts, diamonds, clubs, and spades). Each suit contains the cards ace, 2, 3.., 10, jack, queen, king. a) Find P(E) and P (E'). b) Find P(F) and P (F'). c) Find P(EUF).

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS