Lectures Applied statistics for business: Chapter 4 - ThS. Nguyễn Tiến Dũng

Lectures "Applied statistics for business - Chapter 4: Introduction to probability" provides students with the knowledge: Experiments, counting rules and assigning probabilities, events and their probabilities, some basic relationships of probability, conditional probability, bayes’ theorem. Invite you to refer to the disclosures.
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Lectures Applied statistics for business: Chapter 4 - ThS. Nguyễn Tiến Dũng Chapter 4INTRODUCTION TO PROBABILITY Nguyen Tien Dung, MBA School of Economics and ManagementWebsite: https://sites.google.com/site/nguyentiendungbkhn Email: dung.nguyentien3@hust.edu.vnMain Contents4.1 EXPERIMENTS, COUNTING RULES AND ASSIGNING PROBABILITIES4.2 EVENTS AND THEIR PROBABILITIES4.3 SOME BASIC RELATIONSHIPS OF PROBABILITY4.4 CONDITIONAL PROBABILITY4.5 BAYES’ THEOREM© Nguyễn Tiến Dũng Applied Statistics in Business 24.1 EXPERIMENTS, COUNTING RULES,AND ASSIGNING PROBABILITIES ● Sample space for an experiment: ● the set of all experiment outcomes ● An experiment outcome is also called a sample point© Nguyễn Tiến Dũng Applied Statistics in Business 3Probability As A Numerical Measure Of TheLikelihood Of An Event Occurring ● S = {Head; Tail} ● S = {Defective, Nondefective} ● S = {1, 2, 3, 4, 5, 6}© Nguyễn Tiến Dũng Applied Statistics in Business 4Counting Rules, Combinations, and Permutation● Counting Rules ● Being able to identify and count the experimental outcomes is a necessary step in assigning probabilities.● Multiple-step experiments ● Example 1: Toss 2 coints ● Example 2: Kentucky Power & Light Company Construction Project (KP&L Project) ● Tree diagram ● a graphical representation that helps in visualizing a multiple-step experiment.© Nguyễn Tiến Dũng Applied Statistics in Business 5The Tree Diagram For the Tossing-2-CointExperiment© Nguyễn Tiến Dũng Applied Statistics in Business 6The Tree Diagram for the KP&L Project© Nguyễn Tiến Dũng Applied Statistics in Business 7Combinations ● Example: There are 4 football teams, playing in a tournament. Each will meet the rest once. How many football matches will the tournament have? ● Do it in 2 ways: manually and using C(N,n).© Nguyễn Tiến Dũng Applied Statistics in Business 8Permutations ● Example: There are 5 digits: 1, 2, 3, 4, 5. How many two-digit numbers could be formed from these five digits.© Nguyễn Tiến Dũng Applied Statistics in Business 9Assigning Probabilities© Nguyễn Tiến Dũng Applied Statistics in Business 10Assigning Probabilities● Classical method ● No. of favourable outcomes (computation) / Total possible outcomes ● When all experimental outcomes are equally likely● Relative frequency ● Actual data ● Frequency of occurrences of interested outcomes / Total actual outcomes● Subjective method ● A method of assigning probabilities on the basis of judgment© Nguyễn Tiến Dũng Applied Statistics in Business 11Classical method● Appropriate when all the experimental outcomes are equally likely.● If n experimental outcomes are possible, a probability of 1/n is assigned to each experimental outcome.● Example 1: toss a coin● Example 2: roll a dice© Nguyễn Tiến Dũng Applied Statistics in Business 12 Relative frequency method Number of Number of Days Waiting Outcome Occurred ● Appropriate when data are 0 2 available to estimate the proportion of the time the 1 5 experimental outcome will occur 2 6 if the experiment is repeated a 3 4 large number of times. 4 3 Total 20 ● Example: a study of waiting times Number of Probability of in the X-ray department for a local Waiting Outcome Occurred hospital. A clerk recorded the 0 2/20 = 0.1 number of patients waiting for 1 5/20 = 0.25 service at 9:00 a.m. on 20 2 6/20 = 0.3 successive days and obtained the 3 4/20 = 0.2 following results. 4 3/20 = 0.15 Total 20/20 =1.00© Nguyễn Tiến Dũng Applied Statistics in Business 13AssigningProbabilitiesby the RelativeFrequencyMethod© Nguyễn Tiến Dũng Applied Statistics in Business 144.2 EVENTS AND THEIR PROBABILITIES● An event is a collection of sample points● KP&L Project ● C = {(2,6), (2, 7), (2,8), (3,6), (3,7), (4,6)} ● Event C includes many sample points ● One event may be comprised of many events ● L = the event that the projects is completed in LESS than 10 months ● L = {(2,6), (2,7), (3, 6)} ● M = the event that the project is completed in 10 months or more than 10 months ● M = {(2,8), (3,7), (4,6) ● C = {L, M}● Probability of an event ● The sum of the probability of the sample points in the event.© Nguyễn Tiến Dũng Applied Statistics in Business 15 4.3 SOME BASIC RELATIONSHIPS OF PROBABILITY ● Complement of an event ● P(A) = 1 – P(Ac)© Nguyễn Tiến Dũng Applied Statistics in Business 16Union of Two Events ● The union of A and B is the event containing all sample points belonging to A or B or both. The union is denoted by A  B.© Nguyễn Tiến Dũng Applied Statistics in Business 17Intersection of Two Events● Given two events A and B, the intersection of A and B is the event containing the sample points belonging to both A and B. The intersection is denoted by A B.© Ng ...