This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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;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 &quot;Bourne Ultimatum&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; 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....
View
Full Document
 Spring '08
 BATEH
 Statistics, Probability theory, discrete random variable

Click to edit the document details