Suppose there exists a Facebook group of n profiles, where n > 2. Within this group,there are some friendship connections. A member of the group could be friends with any othermember, or none at all. Prove that, no matter how these friendships are distributed, there willbe at least two members with the same number of friends.

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Answered: Suppose there exists a Facebook group…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose we have a trlangle made of the 3 vertices A, B, and C, and the 3 edges AB, BC, AC. We color each vertex blue or red uniformly at random. Then define 3 random variables (one for each edge) that Indicate whether the edge's vertices are the same color. Are these three random varlables mutually independent?
In a survey of 230 professional athletes, it was found that 117 of them owned a convertible, 105 of them owned a giant screen TV, and 88 owned a sporting goods store. 17 owned a convertible and a store, 34 owned a TV and a store, and 56 owned a covertible and a TV. 8 owned all three items. You must create the Venn Diagram, save it as a pdf and attach your work. How many athletes did not own any of the three items? How many owned a covertible and a TV, but not a store? How many athletes owned a convertible or a TV? How many athletes owned exactly one type of item in the survey? How many athletes owned at least one type of item in the survey? How many owned a TV or a store, but not a convertible?
An advertising agency wants to know whether the no of column inches of classified ad carried by 2 competing newspapers is equal. The no of column inches appearing in both newspapers, respectively, on 20 randomly selected days follows: 663 & 725, 713 & 806, 626 & 620, 682 & 626, 639 & 595, 651 & 614, 769 & 744, 701 & 719, 723 & 680, 670 & 639, 665 & 602, 639 & 657, 694 & 624, 614 & 614, 651 & 583, 632 & 682, 739 & 657, 657 & 639 & 775 & 745. Use signed-rank test at 0.01 level of sig to test to test whether or not newspaper 1 & 2 carry equal amount of classified ad. What is the z value and decision?
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A certain scientific department is called that the students of the department will take the final exams and get points more than 50 points if they are provided with various questions for previous exams in scientific topics To test this claim, 20 students who are expected to graduate were taken and distributed into 10 pairs, so that in each pair there were two students with the same qualifications, and the results of the exam were recorded as follows. 17 (2 575 543 719 591 660 451 579 663 621 531 Students who studied the questions 524 530 748 568 683 424 502 688 540 509 Students who did not study the questions Test the level of significance of 0.05 that looking at the previous exams questions increases the students' grades by at least 50 points.
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