5. Problem 5. (a) Consider a sample space C = {1, 2, 3, 4, 5, 6, 7, 8, 9), whereeach of these numbers are equally probable. Let A be the event all evennumbers. Given A occurred. Compute directly by enumerating A theconditional probability of {1, 2, 3} given A.(b) Suppose A and B are two events that are independent. What can yousay about the independence of each of the following pairs of events: (i) A and Bc(ii) Ac and B, and (iii) Ac and Bc. Show work. (c) Let X be a continuous randomvariable and x be any real number, find the value P[X = x] and give reason for the"answer.*Means the original problem has been modified as described.

Answered: Image /qna-images/answer/ca27ea27-8c47-4739-a827-c2267780e499.jpg

Answered: 5. Problem 5. (a) Consider a sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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7. There are 2,000 cars in City HK, which is divided into Zones A, B, C, and D. For any particular car, the probabilities of being in each zone are given by P(Zone A) = 0.3 P(Zone B) = 0.2 P(Zone C) 0.1 P(Zone D) 0.4.
3. An urn contains 10 red, 15 blue and 25 green balls. (a) Eight balls are chosen without replacement. What is the probability exactly 4 of the chosen balls are green? (b) Now four balls are chosen from the urn without replacement. What is the probability the first chosen ball is red, the second chose ball is green, the third chosen ball is green and the fourth chosen ball is blue?
3)
17) Assume that when adults with smartphones are randomly selected 37%use them in meetings or classes. If 7 adult smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes. The probability is ______.
2. A kindergarten class has 6 boys and 7 girls. At the end of each day, the teacher selects 5 students, uniformly at random, and asks them to help clean up the classroom. One of the boys in the class is named Vito. Show that, with probability = 38%, Vito and at least one girl will be amongst the 5 students asked to clean up today.
1. An experiment is rolling two dice. Show work and give R for “given” probabilities. (a) State the sample space. (b) What is the probability that the sum is 7 given that the first die is a 2? (c)Are the two events sum of 6 and first die is a 5 independent events? Why or why not? (d) Are the two events sum of 7 and first die is a 2 independent events? Why or why not?
The biology department plans to recruit a new faculty member. Data collected by a different university on the 410 possible candidates are available. The biology department is debating whether to put a requirement of 10 years of teaching experience in the job advertisement. The available data on the candidates are shown below. Less than 10 years' 10 or more years' experience experience Total Male 178 112 290 Female 99 21 120 Total 277 133 410 True or False. The events F= {candidate is female} and E = {candidate has less than 10 years' experience} independent. True False
If A and B are two independent events from the sample space s then P (A and B ) = _*_
6. Let A, B, C be three events with P(A) = P(B) = P(C) = 1, P(AC) = 1, P(AB) = P(BC) = 0, determine the probability of the event that at least one of A, B, C occurs.
I choose a random sample of 5 of 20 sofas and I find that all of them are more than $400. If only 10 of these sofas were supposed to be more than $400, what is the probability I would get 5 costing more than $400 in my sample of 5? What would that probability be if 11 of the sofas cost more than $400? Or 12 sofas costing more than $400?
6. Consider en experiment and two events A and B and their complements. The probability of the union of events A and B is precisely 3/4. Moreover, some other probabilities are summarized as follows: A Ac 1/8] B Bc 3/8 (a) Describe the following event in terms of a union or intersection and find their prob- abilities: (i) A is observed and B is not observed. (ii) A is not observed or B is observed. (iii) B is not observed. (b) Assume that event B is observed. What is the probability that A is observed? What is the probability that A is observed assuming Bº is observed? (c) Are A and B independent?

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