5A. Let X and Y are input and output random variables of a binary channel respectively. Let theinput to the channel is defined by an alphabet, X = {0,1} and the output of the channel is1/10defined by an alphabet, Y = {0,1}. This channel is characterized by P = 1/20 19/20[9/10If%3DP(X = 0) = 3/4, Compute(i) Probability Matrices, P(X,Y) and P(X/Y)(ii) H(X/Y = 0), H(X/Y = 1)(iii) H(X/Y),H(Y/X), and Mutual Information

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Answered: 5A. Let X and Y are input and output…

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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A cigarette company wants to promoe thne sales of X's cigarettes (Brand) with special advertising campaign. Fifty out of every thousand cigarettes are rolled up in gold foil and randomly mixed with the regular (special king-sized, mentholated) cigarettes. The company offers to trade a new package of cigarettes for each gold cigarette a smoker finds in a package of Brand X. What is the probability that buyers of Brand X will find X = 0, 1, 2, 3, . gold cigarettes in a single package of 10 ? ...
Suppose the random variables X,, X,,X3 have the population variance/covariance matrix: -2 0 E=-2 5 1 Calculate the principal components and interpret their meaning. What can be gained from knowing these values?
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sar Suppose that we also have the following. E(X)=-5 E(Y)=8 E(Z)=6 Var (X)=24 Var (Y) = 16 Var (Z) = 33 Compute the values of the expressions below. E (4Y+4)= 36 E(-4Z+2X)- -3 = 11.33 Var (4Y)-2= 254 E(-x²) = 49 0|0 X
= 3. Propose an algorithm for simulating the occurrence of two dependent events A and B that uses only one uniform random variable U~Unif(0, 1). Assume that the probabilities P(A) ΡΑ, P(B) = PB, and P(AUB) = q are given, where PA, PB, q = (0, 1) and max(PA, PB) < q < PA+PB· Formulate your answer in the form of the following statement: "if U E ..., then event A occurs; if U € .……., then event B occurs."
For RBD topology 1, the independent component working probabilities are P(A)0.83, P(B)-0.73, PIC)0.45, PID0.66, P(E0.83. What is the probability that the system will work? Your answer: O 0.382043 O 0.520173 O 0,436623 O 0.929271 O 0.903641 O 0.152346 O 0,952901 O 0728327
I was wondering if you could help me understand how to find the probability of failure of the entire deck system assuming that the failures of groups A, B and C are independent of each other and that the failures of sub-groups B1 and B2 are also independent of each other
Let (X1, X2, X3) be the random outcome of tossing a fair six-faced die three times, and let (Y(1), Y(2), Y(3) be the order statistics from (X1, X2, X3). We have Y(1) = min (X1, X2, X3), Y(3) = max (X1, X2, X3), and Y(1) < Y(2) < Y(3). Find Pr (Y(1) = 3).
8. List the Gauss–Markov conditions required for applying a t & F-tests.
Use the data in the table below, which shows the employment status of individuals in a particular town by age group. Part-time Unemployed Age Full-time 0-17 25 187 252 18-25 391 200 199 26-34 434 66 22 35-49 562 192 149 50+ 461 170 237 If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?
please be clear
1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)– P(BnC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC) = 1– P(A^)P(B^)P(C*) = 1– (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 2/5, the probability that B hits it is 5/9, and the probability that C hits the target is 3/7. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p > 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1 — р)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0006 and n = 750, and then round your result to a…
5) A Professor conducts an exam in a class with 24 boys and 16 girls. 6 boys and 4 girls make an A in the course. a) Write the joint pohahility matrix of the gender of the student and his/her grade (A or no A). b) Find the marignal probabilities of a student being a boy or a girl and the marginal probabilities of a student making or not making an A in the course. Show that the gender of a student and whether he/she makes an A in the course, are independent.

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