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Random Variables and Probability Distributions

POLI 270 - Mathematical and Statistical FoundationsProf. S. SaieghFall 2010 Lecture Notes - Class 8 November 18, Variables and Probability DistributionsWhen we perform an experiment we are often interested not in the particular outcomethat occurs, but rather in somenumberassociated with that example, in the game of craps a player is interested not in the particular numberson the two dice, but in theirsum. In tossing a coin 50 times, we may be interested only inthenumberof heads obtained, and not in the particular sequence of heads and tails thatconstitute the result of 50 both examples, we have a rule which assigns to each outcome of the experiment asingle real number.

De nition 2 The function f whose value for each real number xis given by (2), or equiva-lently by (1), is called the probability function of the random variable X.

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