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# 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.
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.
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 The last row of Table 2.1 gives the cumulative probability distribution of M .
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ch2-1 - Chapter 2 Review of Probability(Part 1...

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