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prob.part4.9_10

# prob.part4.9_10 - Chapter 1 Discrete Probability...

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Chapter 1 Discrete Probability Distributions 1.1 Simulation of Discrete Probabilities Probability In this chapter, we shall first consider chance experiments with a finite number of possible outcomes ω 1 , ω 2 , . . . , ω n . For example, we roll a die and the possible outcomes are 1, 2, 3, 4, 5, 6 corresponding to the side that turns up. We toss a coin with possible outcomes H (heads) and T (tails). It is frequently useful to be able to refer to an outcome of an experiment. For example, we might want to write the mathematical expression which gives the sum of four rolls of a die. To do this, we could let X i , i = 1 , 2 , 3 , 4 , represent the values of the outcomes of the four rolls, and then we could write the expression X 1 + X 2 + X 3 + X 4 for the sum of the four rolls. The X i ’s are called random variables . A random vari- able is simply an expression whose value is the outcome of a particular experiment. Just as in the case of other types of variables in mathematics, random variables can take on di ff erent values. Let X be the random variable which represents the roll of one die. We shall assign probabilities to the possible outcomes of this experiment.

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prob.part4.9_10 - Chapter 1 Discrete Probability...

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