5. 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 a 1 wassent? Derive an expression for the probability of a transmission error.P(R1IT1) =1-oaT1R1a/2a /2B/21-BT2R2B/2Y/2Y/21-yT3R3Figure 1.P.6. A trinary communication channel: channel diagram

Given the trinary communication channel:

Answered: 5. 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...

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8. Let A, B be two events with P(A) = ½, P(A − B) = 3, determine P(AB).
Cynthia is president of an international chemical distribution company, Cchem. Weekly gross sales for Cchem has a mean of $1 million and standard deviation of $0.2 million; the distribution of sales is highly right-skewed. One week’s sales are independent of the sales in any other week. Use this information to answer questions 5 to 6 below. What is the probability that sales for the week of October 5, 2009 will be more than $1.25 million? In order for Cynthia to receive a bonus, Cchem’s annual sales must exceed $53 million. What is the probability that Cynthia will receive a bonus for the fiscal year starting in 2010? Assume there are 52 weeks in a year.
1. Let A and B be two events such that ACB, then P(AB)= 1,2,3/Q1. (22 points)] This question consists of 11 paragraphs. In each part, circle the correct an a. P(A) d.0 b. P(A) c. P(B) 2. How many different four-digit numbers can be formed from the digits 1,2,3,4,5,6,7 such that the first digit 3 or 6 also you cannot repeat the digit. a. 240 b.48 c. 120 3. If A, B and C are mutually independent events and that P(A) = 0.3, P(B) = 0.2, P(C) = 0.4. The probability that at least one of the events occur is a. 0.336 c. 0.024 b.0.664 d. 0.976 e. None 4. A box contains 3 red balls and 5 black balls. Balls are drawn randomly one at a time with replacement from the box. The probability that the third red ball is the seventh ball drawn is. a. 0.169 b.0.282 c. 0.179 d. 0.121 e. None 5. A box contains 20 balls, 13 of them are red and the rest are blue. Three balls are drawn randomly without replacement. The probability of getting at least I blue ball is. a) 0.749 b) 0.251 c) 0.479 d) 0.521 a. 0.4 b.…
The highways connecting two resorts at A and B are sometimes closed due to snow and ice. Let E,, E, and E, denote the events that highways AB and AC and CB are passable, respectively. From past years' records: 3 P(E,) =. P(E,) =, P(E,) =, =. 4 P(E,\ E,) = and P[E, |(E,nE,)]= 4 What is the probability that a traveler will be able to get from A to B? E, E2 Hint: Define E: the event that a traveler can get from A to B E= E, U(E,E), and %3D compute P(E) to find the probability that a traveler will be able to get from A to B, ie. P(E), for this computation use the definition of conditional probability and compute P(E) to find the probability that a traveler will be able to get from A to B, i.e. P(E), for this computation use the definition of conditional probability.
What would be the correct way of doing this?
V. (10) The following table of 850 students shows those that have or don't have covid-19 and shows those who had a positive test or a negative test. I just made this data up so don't take this as representative of our current state. Answer the following questions. Negative Test 5 Positive Test Have Covid-19 45 Don't have Covid-19 25 775 Let D be the event you Don't have Covid-19 and N the event you have a negative test. 1. P(D) = 2. P(D I N) = 3. Are D and N independent? 5. What is the probability that you Have Covid-19 even though the test came back negative? 4. Explain TI-84 Plus TEXAS INSTRUMENTS
Please answer d and e. P.9.2
2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 by more than 1/4" and "1-U is less than 1/2", respectively. Find the events An B, Ān B, AU B.
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
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.
2. Page 34, 1.4.14*. Each of three persons fires one shot at a target. Let Ck denote the event that the target is hit by person k, k = 1, 2, 3. If C1, C2, C3, are independent and if P(C1) = P(C2) = 0.8, and P(C3) = 0.9, compute the probability that (a) all of them hit the target; (b) exactly one hits the target; (c) no one hits the target; (d) at least one hits the target.
Let (A,n 2 1) be independent events. Then a)E=1 P(A,) = 0 == P(A i.o.) = 1 b) En=1 P(A,)<=P(A, i.o.) = 0.

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