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This 3 page Class Notes was uploaded by Debra Tee on Monday October 3, 2016. The Class Notes belongs to STATS 250 at University of Michigan taught by Brenda Gunderson in Fall 2016. Since its upload, it has received 2 views. For similar materials see Introduction to Statistics in Statistics at University of Michigan.
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Date Created: 10/03/16
Lecture 5: Probability 7.1 Random Circumstance and Interpretations of Probability - A few ways to think about PROBABILITY: (1) Personal or Subjective Probability - P(A) = the degree to which a given individual believes that the event A will happen. (2) Long term relative frequency P(A) = proportion of times ‘A’ occurs if the random experiment (circumstance) is repeated many, many times. (3) Basket Model P(A) = proportion of balls in the basket that have an ‘A’ on them. - Note: each time I do the experiment, the selected ball is either white or blue;; once I look, there is no more ‘probability’) - Note: A probability statement IS NOT a statement about INDIVIDUALS. It IS a statement about the population / the basket of balls . 7.3 Probability Definitions and Relationships 7.4 Basic Rules for Finding Probability - probability of any outcome is always between 0 and 1 Probability Rules and Formulas -‐ Complement rule P(AC ) ▯ 1 - P(A) -‐ Addition rule P(A or B) = P(A) + P(B) -▯ P(A and B) -‐ Multiplication rule P(A and B) =▯ P(A)P(B | A) -‐ Conditional Probability P(AB) = P(A and B)/P(B) Definition: -‐ Two events A, B are Mutually Exclusive (or Disjoint) if they do not contain any of the same outcomes. So their intersection is empty. -‐ Two events A, B are said to be independent if knowing that one will occur (or has occurred) does not change the probability that the other occurs. In probability notation this can be expressed as P(A|B) = P(A). Sampling with and without Replacement Definitions: A sample is drawn with replacement if individuals are returned to the eligible pool for each selection. A sample is drawn without replacement if sampled individuals are not eligible for subsequent selection. -‐ If a sample is drawn from a very large population, the distinction between sampling with and without replacement becomes unimportant. -‐ Sometimes students confuse the mutually exclusive with independence. The definition for two events to be disjoint (mutually exclusive) was based on a SET property. ▯ -‐ The definition for two events to be independent is based on a PROBABILITY property. -‐ You need to check if these definitions hold when asked to assess if two events are disjoint, or if two events are independent.