Yahoo India Web Search

Search results

1. • Boole's inequality

     • In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events.
     en.wikipedia.org/wiki/Boole's_inequality

     Boole's inequality - Wikipedia

2. People also ask

   What is a union bound?

   • The union bound, though seemingly trivial, can actually be quite useful. This will relate to the earlier question of bounding the probability of at least one bad event happening. Suppose the probability Alex is late to teaching class on a given day is at most 0:01. Bound the probability that Alex is late at least once over a 30-class quarter.

   6.3.1 The Union Bound - University of Washington

   courses.cs.washington.edu/courses/cse312/20su/files/student_drive/6.3.pdf

   See all results for this question

   When is the union bound A Boole's inequality?

   • The union bound or Boole's inequality [ 13] is applicable when you need to show that the probability of union of some events is less than some value. Remember that for any two events A and B we have P(A ∪ B) = P(A) + P(B) − P(A ∩ B) ≤ P(A) + P(B). Similarly, for three events A, B, and C, we can write ≤ P(A) + P(B) + P(C).

   The Union Bound and Extension - Course

   www.probabilitycourse.com/chapter6/6_2_1_union_bound_and_exten.php

   See all results for this question

   How to write a union bound using induction?

   • P(A ∪ B) = P(A) + P(B) − P(A ∩ B) ≤ P(A) + P(B). Similarly, for three events A, B, and C, we can write ≤ P(A) + P(B) + P(C). ≤ P ( A) + P ( B) + P ( C). In general, using induction we prove the following The union bound is a very simple but useful result. It is used frequently in different applications.

   The Union Bound and Extension - Course

   www.probabilitycourse.com/chapter6/6_2_1_union_bound_and_exten.php

   See all results for this question

   What is a union bound in random graphs?

   • The union bound is a very simple but useful result. It is used frequently in different applications. Here, we look at one application in the area of random graphs. Random graphs are widely used when analyzing social networks, wireless networks, and the internet. A simple model for random graphs is the Erdös-Rényi model G(n, p) [ 11, 12 ].

   The Union Bound and Extension - Course

   www.probabilitycourse.com/chapter6/6_2_1_union_bound_and_exten.php

   See all results for this question

3. en.wikipedia.org › wiki › Boole's_inequalityBoole's inequality - Wikipedia

   en.wikipedia.org › wiki › Boole's_inequality

   • Cached

   In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events.

4. www.probabilitycourse.com › chapter6 › 6_2_1_unionThe Union Bound and Extension - probabilitycourse.com

   www.probabilitycourse.com › chapter6 › 6_2_1_union

   • Cached

   Learn how to use the union bound and its extension, the Bonferroni inequalities, to bound the probability of union of events. See examples of applications in random graphs and expected value of events.

5. Images

   • 
   • 
   • 
   • 

   View all

6. courses.cs.washington.edu › courses › cse3126.3.1 The Union Bound - University of Washington

   courses.cs.washington.edu › courses › cse312

   Learn how to use the union bound to bound the probability of multiple events occurring, and how to apply Jensen's inequality and Hoe ding's inequality to convex functions. See examples, proofs, and slides from CSE312 course at UW.

   • File Size: 702KB

   • Page Count: 8

7. probability.oer.math.uconn.edu › wp-contentProbability inequalities - University of Connecticut

   probability.oer.math.uconn.edu › wp-content

   Boole's inequality (or the union bound ) states that for any at most countable collection of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the events in the collection.

   • File Size: 366KB

   • Page Count: 14

8. nanjiang.cs.illinois.edu › files › cs542Concentration Inequalities and Union Bound

   nanjiang.cs.illinois.edu › files › cs542

   Learn how to use Hoeffding's inequality and union bound to analyze the performance of learning algorithms. See examples of MAB, generalization bounds, and lower bounds.

   • File Size: 220KB

   • Page Count: 4

9. ocw.mit.edu › courses › 18-s997-high-dimensionalChapter 1: Sub-Gaussian Random Variables - MIT OpenCourseWare

   ocw.mit.edu › courses › 18-s997-high-dimensional

   The second inequality follows from symmetry and the last one using the union bound: IP(|Z| >t) = IP({Z>t}∪{Z< −t}) ≤ IP(Z>t)+IP(Z< −t) = 2IP(Z>t). The fact that a Gaussian random variable Z has tails that decay to zero exponentially fast can also be seen in the moment generating function (MGF)

10. www.cs.princeton.edu › courses › archive1 Comment on Union Bound - Princeton University

    www.cs.princeton.edu › courses › archive

    In the previous lecture in which probabilities were discussed, the Union Bound property of random variables was discussed. In its basic form, this rule in whichAandBare random variables states the following: Pr[A_B] Pr[A]+Pr[B] IfAandBare disjoint then this will result in equality.