A binary message (0 or 1) is transmitted through a noisy channel. Let X bethe message transmitted, and let Y be the message received.Suppose that X = 0 and X = 1 is transmitted with equal probability andsuppose that the receiver obtains the message correctly 90% of the time.True or False: X and Y are independent random variables.Select one:O TrueFalse

Answered: A binary message (0 or 1) is…

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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Fill in the gaps with one or more words: A.B,M and X are random variables. If A and B are independant then they _____ uncorrelated. If E(MX)= E(M)E(X) then M and X _____ independant.
Two players, A and B, alternately and independently flip a coin for a game. The game has up to a total of 5 flips and the first player to obtain a head wins. Assume player A flips first. The coin is unfair with P(head) = 2/3. Find the probability that player A wins
A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
A car can travel from Town A to Town C by using the four roads below. The probabilities of these roads being closed are P(H1), P(H2), P(H3) and P(H4). Calculate the probability that a car cannot reach Town C from Town A, knowing that the closure of the roads are independent from each other. H1 H3 TOWN A TOWN B TOWN C H2 Н4
Suppose a and b be two possible values of a random variable X with a > b. The probability that X lies between a and b is P(a > X > b) = F (a) - F (b) Select one: O True O False
You are the teacher of two math classes of 20 and 25 students respectively. To get into a university program, the students need a 75% in the class. Suppose each student has a 0.7 probability of getting atleast a 75% in the class. Let X1 be the number of students in the class of 20 who receive atleast a 75%. Let X2 be the number of students in the class of 25 who receive atleast a 75%. a. Do X1 and X2 fit the binomial setting? Are there any issues? For the rest of the question, assume both X1 and X2 can be modeled by a binomial distri- bution. b. What is the probability that exactly 15 students in the class of 20 get into the pro- gram? Do not use Table C. c. What is the probability that atleast 22 students in the class of 25 get into the pro- gram? Do not use Table C. d. Using Table C, what is the probability that atleast 17 students in the class of 20 get into the program? е. Let X be the number of students in both classes that get into the program. Deter- mine the mean and standard…
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is tth, then =Rtth1. Suppose that the random variable X is defined in terms of R as follows: =X−R2−3R4. The values of X are given in the table below. Outcome htt tht hth thh ttt hhh hht tth Value of X −6 −6 −6 −6 −4 −4 −6 −6 Calculate the values of the probability distribution function of X, i.e. the function p X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.
Suppose there are exactly three states of weather: sunny, cloudy, or rainy. If it is sunny today, then the probability is 3/4 that it will be sunny tomorrow, 1/8 that it will be cloudy tomorrow, and 1/8 that it will be rainy. If it is cloudy today, then the probability is 1/2 that it will be sunny tomorrow, 1/4 that it will be cloudy tomorrow, and 1/4 that it will be rainy. If it is rainy today, then the probability is 1/4 that it will be sunny tomorrow, 1/2 that it will be cloudy tomorrow, and 1/4 that it will be rainy. cloudy is From this Markov model, for any given day the probability that it will be sunny is rainy is Round your answers to three decimal places. and
Each of the random variables X and Y takes only 3 values {1,2,3} with the following probabilities: 1 1 0 1/6 1/6 y 2 1/6 0 1/6 3 1/6 1/6 0 2.
A fair dice is thrown once. The random variable Y is related to the number B thrown on the dice as follows. If B is even, then Y is half B, otherwise Y is triple B. Find the mode and E(Y). Select one: no mode and E(Y) = - mode = 3 and E(Y) = 4 mode = 2 and E(Y) = mode = 3 and E(Y) = mode = 5 and E(Y) =

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