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Statistics 401, Weeks 5 & 6

by: Wendy Liu

Statistics 401, Weeks 5 & 6 01:960:401

Marketplace > Rutgers University > Statistics > 01:960:401 > Statistics 401 Weeks 5 6
Wendy Liu
GPA 4.0

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About this Document

Covers intro to probability, counting rules, probability for independent and non-independent events, etc.
Basic Statistics for Research
Hei-ki Dong
Class Notes
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This 2 page Class Notes was uploaded by Wendy Liu on Thursday October 13, 2016. The Class Notes belongs to 01:960:401 at Rutgers University taught by Hei-ki Dong in Fall 2016. Since its upload, it has received 25 views. For similar materials see Basic Statistics for Research in Statistics at Rutgers University.

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Date Created: 10/13/16
Week 5 & 6: Probability 4 October 2016, 11 October 2016 Basic Statistics for Research Professor HK Dong Wendy Liu Probability – numerical measure of the likelihood an event will occur  Lies between 0 and 1  Sum of all probabilities of all possible outcomes is 1 Method 1: approximation  Empirical frequency obtained by experimentation Method 2: actual calculation  Classical, accurate probability P probability A, B,… denotes specific event P(A) denotes probability of event A Experiment – process of observing an event that has variable outcomes, and each single outcome cannot be predicted w/ certainty Ex: toss a dice Sample point – each single outcome of an experiment Ex: {1} {2} {3} {4} {5} {6} Sample space – collection of all possible outcomes Ex: {1, 2, 3, 4, 5, 6} Events – desired outcome(s) Ex: even{2, 4, 6} odd{1, 3, 5} {3, 4, 5, 6} Visual representations of probability  Listing  Venn diagram  Tree diagram  Contingency/two-way table Complement (Ā) – set of all outcomes that are not in A Union (A ∪ B) – set of all outcomes that are in A, B, or both Intersection (A ∩B) – set of all outcomes that are in both A and B Mutually exclusive – intersection A ∩ B is empty; no outcomes in common Law of Complement: Addition Rule: probability of A or B: ∪ Multiplication Rule: probability of A and B: Addition Rule for Mutually Exclusive events: ∪ Multiplication Rule for mutually exclusive events: Conditional probability – event probability given that another event occurred  Revise original sample space to account for new info  Eliminates certain outcomes P of A given B: Tests for independence: A and B are independent if  B has no influence on A:  A has no influence on B:  Total Probability: Baye’s Rule – given k mutually exclusive & exhaustive events such that and an observed event A, then  Permits revising old probabilities based on new info o Prior probability – associated w/ B and before we know status of A  and o Posterior probability – updated probability of B   Application of conditional probability  Mutually exclusive events Combinations – number of possible choices of r objects from a group of N distinct objects Permutations – number of possible selections of k objects from a group of N distinct objects in which the selection order matters


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