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Lecture 2

Week 2 EC255.docx

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Wilfrid Laurier University
Alex Lun

EC255 Week 2 4.1 INTRODUCTION TO PROBABILITY -Much statistical analysis is inferential, and probability is the basis for inferential statistics 4.2 METHODS OF ASSIGNING PROBABILITIES Classical Method of Assigning Probabilities -This method involves an experiment, which is a process that produces outcomes, and an event, which is an outcome of an experiment -When we assign probabilities using the classical method, the probability of an individual event occurring is determined as the ratio of the number of items in a population containing the event, to the total number of items in the population Relative Frequency of Occurrence -The probability of the event occurring is equal to the number of times the event has occurred in the past divided by the total number of opportunities for the event to have occurred Subjective Probability -Based on the feelings or insights of the person determining the probability -Comes from the person’s intuition or reasoning 4.3 STRUCTURE OF PROBABILITY Experiment -A process that produces outcomes Event -An outcome of an experiment -The experiment defines the possibilities of the event Elementary Events -Events that cannot be decomposed or broken down into other events -Denoted by lowercase letters -Ex. In the experiment of rolling a die, there are six elementary events Sample Space -A complete roster or listing of all elementary events for an experiment -The sample space for the roll of a single die is {1, 2, 3, 4, 5, 6} Unions and Intersections -The union of X and Y is formed by combining elements from both sets and is denoted X u Y – combine the possibilities of both into one listing -The intersection contains the elements common to both sets – Ex. The middle of the venn diagram EC255 Week 2 Mutually Exclusive Events -Two or more events are mutually exclusive events if the occurrence of one event precludes the occurrence of the other event(s) -This characteristic means that mutually exclusive events cannot occur simultaneously and therefore can have no intersection Independent Events -Two or more events are independent evens if the occurrence or non-occurrence of one of the events does not affect the occurrence or non-occurrence of the other event(s) -Certain experiments, such as rolling dive, yield independent events, each die is independent of the other -Coin tosses are independent of each other Collectively Exhaustive Events -Contains all possible elementary events for an experiment -Thus all sample space are collectively exhaustive lists Complementary Events -The complement of event A is denoted A’, pronounced “not A” -All the elementary events of an experiment not in A make up its complement -If event A is getting a 5 on the roll of a die, the complement of A is getting 1, 2, 3, 4, 6 Counting the Possibilities -The mn counting rule – for an operation that can be
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