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# Notes 7 - Notes 7 Random Variables A random variable(r.v is...

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Unformatted text preview: Notes 7 Random Variables A random variable (r.v.) is a function whose values are 1) numerical and 2) depend on the outcomes of a random process. Simply put , a random variable is a quantity whose value depends on chance. &amp;amp;ote : We usually use a capital letter to denote the random variable itself and the corresponding common letter to represent the value which the variable takes. Eg. Y = y A random variable assumes exactly one numerical value for each outcome of the random process. The SAMPLE SPACE (S) of a random variable is the set of all possible values that the random variable can take. Examples: X= the number of people who have been to a movie V = the liquid volume of soda in a can marked 12 oz. A discrete random variable has a finite or countable number of possible values. i.e. the sample space consists of a finite number of values (or an infinite number of values that are countable). Example: Three people are chosen at random and asked if they have seen the movie &amp;quot;Bourne Ultimatum&amp;quot;. Define the r.v. : Let X = the number of people (out of the 3) who have seen the Bourne Ultimatum (i.e. the yes answers) Sample Space : S = {0, 1, 2, 3} (These are all the possible values that X can take) The sample space is finite and so X is a discrete r.v. Possible outcomes Yes (Y) and No (N) YYY YYN YNY YNN NYY NYN NNY NNN Corresponding values of X 3 2 2 1 2 1 1 0 If we assume that each person is equally likely to answer YES or !O, then the eight outcomes above are all equally likely to occur. Notes 7 PROBABILITY DISTRIBUTIO&amp;amp; of a random variable The probability distribution of a random variable gives a listing of the possible values of the variable and the corresponding probabilities for those values....
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Notes 7 - Notes 7 Random Variables A random variable(r.v is...

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