ch2-1 - Chapter 2 Review of Probability (Part 1)...

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Chapter 2 Review of Probability (Part 1)
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Probabilities, the Sample Space, and Random Variables Suppose that you are writing a term paper, and worrying how many times your computer will crash. I The numbers of times your computer will crash have an element of randomness . I Your computer might never crash, it might crash once, it might crash twice, and so on. I Only one of these outcomes will actually occur. I Outcomes : The mutually exclusive potential results of a random process. If you could complete 80 out of 100 term papers without crash, the probability of your computer not crashing while you are writing term paper is 80%. I Probability : The probability of an outcome is the proportion of the time that the outcome occurs in the long run.
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Probabilities, the Sample Space, and Random Variables Suppose that the number of times your computer will crash is twice at most. I Then the sample space is the set consisting of all three possible outcomes: "no crashes", "one crash" and "two crashes." I Sample space : The set of all possible outcomes. The event "my computer will crash no more than once" is the set consisting of two outcomes: "no crashes" and "one crash." I Event : An event is a subset of the sample space (a set of one or more outcomes).
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Probabilities, the Sample Space, and Random Variables The number of times your computer crashes while you are writing a term paper is random and takes on a numerical value, so it is a random variable . I Random variable : A numerical summary of a random outcome. I A discrete random variable takes on only a discrete set of values. I A continuous random variable takes on a continuum of possible values.
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Probability Distribution of a Discrete Random Variable Let M be the number of times your computer crashes while you are writing term paper. I The second row of Table 2.1 is the list of probabilities of each possible outcome, the probability distribution of the random variable M . I Probability distribution : The list of all possible values of the variable and the probability that each value will occur. These probabilities sum to 1. The probability that M = 0 is denoted by Pr ( M = 0 ) , the probability that M = 1 is denoted by Pr ( M = 1 ) , and so forth. I Pr ( M = 0 ) = 0.80, or 80%; Pr ( M = 1 ) = 0.10, or 10%. This probability distribution is plotted in Figure 2.1.
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Probability Distribution of a Discrete Random Variable The probability of the event "my computer will crash no more than once" can be computed from the probability distribution: I Pr ( M = 0 or M = 1 ) = Pr ( M = 0 ) + Pr ( M = 1 ) = 0.90, or 90%. Cumulative probability distribution : The probability that the random variable is less than or equal to a particular value. Also referred to as a cumulative distribution function ( c.d.f. ) or a cumulative distribution . I
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This note was uploaded on 11/20/2011 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Fall '10 term at Rutgers.

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ch2-1 - Chapter 2 Review of Probability (Part 1)...

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