1 / 8

C3: Conditional Probability And Independence

MATH 3033 based on Dekking et al. A Modern Introduction to Probability and Statistics. 2007 Slides by James Connolly Instructor Longin Jan Latecki . C3: Conditional Probability And Independence. 3.1 – Conditional Probability.

eytan
Télécharger la présentation

C3: Conditional Probability And Independence

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. MATH 3033 based onDekking et al. A Modern Introduction to Probability and Statistics. 2007Slides by James Connolly Instructor Longin Jan Latecki C3: Conditional Probability And Independence

  2. 3.1 – Conditional Probability • Conditional Probability: the probability that an event will occur, given that another event has occurred that changes the likelihood of the event • Example:If event L is “person was born in a long month”, and event R is “person was born in a month with the letter ‘R’ in it”, then P(R) is affected by whether or not L has occurred. The probability that R will happen, given that L has already happened is written as: P(R|L)

  3. 3.1 – Conditional Probability Provided P(C) > 0 3.2 – Multiplication Rule For any events A and C:

  4. 3.3 – Total Probability & Bayes Rule The Law of Total Probability Suppose C1, C2, … ,CM are disjoint events such that C1 U C2 U … U CM = Ω. The probability of an arbitrary event A can be expressed as:

  5. 3.3 – Total Probability & Bayes Rule Bayes Rule: Suppose the events C1, C2, … CM are disjoint and C1 U C2 U … U CM = Ω. The conditional probability of Ci, given an arbitrary event A, can be expressed as: or

  6. 3.4 – Independence Definition: An event A is called independent of B if: That is to say that A is independent of B if the probability of A occurring is not changed by whether or not B occurs.

  7. 3.4 – Independence Tests for Independence To show that A and B are independent we have to prove just one of the following: A and/or B can both be replaced by their complement.

  8. 3.4 – Independence Independence of Two or More Events Events A1, A2, …, Am are called independent if: This statement holds true if any event or events is/are replaced by their complement throughout the equation.

More Related