1 / 7

Discrete Mathematics CS 2610

Discrete Mathematics CS 2610. November 5, 2008. Probability Theory. When dealing with experiments for which there are multiple outcomes- x 1 , x 2 , …, x n –we require 0  p( x i )  1 for i = 1, 2, …, n and (i=1, n) p( x i ) = 1

keelty
Télécharger la présentation

Discrete Mathematics CS 2610

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discrete Mathematics CS 2610 November 5, 2008

  2. Probability Theory • When dealing with experiments for which there are multiple outcomes- x1, x2, …, xn –we require • 0  p(xi)  1 for i = 1, 2, …, n and • (i=1, n) p(xi) = 1 • We can treat p as a function that maps elements from the sample space to real values in the range [0,1]. We call such a function a probability distribution.

  3. Probability Theory Uniform Probability Distribution: p(xi) = 1/n, for i = 1, 2, …, n All outcomes are equally probable.

  4. Probability Theory Note that sum and product rules apply when dealing with probabilities too! Sequences of events are products Either/or requires sum rule and subtraction principle Complementary rule works too!

  5. Conditional Probability The conditional probability of E given F is P(E | F) = p(E  F) / p(F) This is the probability that E will/has occurred if we know that F has/will occur.

  6. Independence Two events, E and F, are independent iff p(E1  E2) = p(E1) p(E2) The two events don’t influence one another!

  7. Repeated trials If there are a number of trials being conducted, each of which has a probability of success of p and a probability of failure of q = 1 – p, then the probability of exactly k successes in n independent trials is C(n,k)pkqn-k This is called the binomial distribution.

More Related