MBA 5020 Week 4 Lecture Notes (Part 2).pdf - WEEK 4 DATA...

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1 WEEK 4: DATA FOR TWO VARIABLES AND PROBABILITY (PART 2) Business managers frequently face uncertain situations and have to base their decisions on an analysis of uncertainties. For example, what is the likelihood that the project can be completed by the due date? What is the chance a new assembly method will increase productivity? What are the odds a new investment will be profitable? To analyze uncertainties to answer these questions, you need to know some basic probability concepts. But first, let's cover some probability definitions. BASIC PROBABILITY CONCEPTS Probability is a measure of the chance that a certain event will occur and is measured on a scale from 0 to 1. A probability value of 0 indicates that the event cannot happen, and a probability value of 1 reveals that the event is sure to happen. A process that results in one of a number of well-defined outcomes that cannot be predicted in advance is called an experiment (random experiment). The listing of all possible outcomes of a random experiment is referred to as the sample space. Any subset of a sample space is called a random event.
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3 ASSIGNING PROBABILITIES Once an event is defined, a probability can be assigned to it. Three approaches of assigning probabilities that are most frequently used are classical, relative frequency, and subjective methods. Classical Method: Classical method is appropriate when all the possible outcomes of an experiment are equally likely to occur. This type of probabilities is classical probability. For example, considering the experiment of rolling a six sided die, it is seasonal to say the six outcomes are equally likely. So if an event is defined as observing even numbers, p(event numbers)=3/6=0.5
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5 Relative Frequency Method: When data are available to estimate the proportion of the time the experimental outcome will occur of the experiment is repeated a large number of times, the relative frequency method (also called empirical probability) is appropriate. This method of assigning probabilities based on experimentation or historical data. This type of probabilities is also called empirical probability. For example, the study of waiting times in the X-ray department for a local hospital shows the number of patients waiting for service on 20 successive days (shown in the following table): Number Waiting Number of Days Outcome Occurred Probability 0 2 2/20=0.1 1 5 0.25 2 6 0.30 3 4 0.20 4 3 0.15 Total 20 1.00 Using the relatively frequency method, the probability of each outcome (number of waiting 0, 1,2,3,4) can be obtained (see the last column of the above table). Then we can figure out probability of union events. P(more than 2 waiting)=P(3 or 4 waiting)=p(s) +p(4) =0.20+0.15=0.35 Subjective Method: When one cannot realistically assume that the outcomes are equally likely and when little relevant data are available, i.e. both classical and relative frequency methods are not appropriate, subjective method should be used.
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