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Unformatted text preview: CHAPTER 3 Random Variable A rule that associate a number to each outcome of an experiment (or each outcome in S ) is random variable. Bernoulli random variable: Any random variable whose only possible values are 0 and 1 Example: Give three examples of Bernoulli random variables.  There is two different types of random variable: Discrete random variable: Possible values are integer. Continuous random variable: Possible values consist of an entire interval on the number line. Example: Three automobiles are selected at random, and each is categorized as having a diesel (S) or nondiesel (F) engine. If X =the number of cars among the three with diesel engine, list each outcome in S and its associated X value. Probability Distribution for Discrete Random Variables The probability distribution of X determine how the total probability is distributed among the values of X . For showing probability distribution can use a formula, graph, or table. The probability distribution or probability mass function for discrete random variable p ( x ) = P ( X = x ) has two conditions: 1. p ( x ) > 2. all possible x p ( x ) = 1  Examples: Airline sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actu ally show up for the flight. The probability mass function of Y appears in the accompanying table. 1 y 45 46 47 48 49 50 51 52 53 54 55 p ( y ) .05 .10 .12 .14 .25 .17 .06 .05 .03 .02 .01 a. What is the probability that flight will accommodate all ticketed passengers who show up? b. What is the probability that not all ticketed passengers who show up can be accommo date? An automobile service facility specializing in engine tuneups knows that 45% of all tune ups are done on four cylinder automobiles, 40% on six cylinder automobiles, and 15% on eightcylinder automobiles. Let X = the number of cylinders on the next car to be tuned. What is the pmf of x ? A Parameter of a Probability Distribution Suppose p ( x ) depends on a quantity that can be assigned any of a number of possible val ues, with each different value determining a different probability distribution. Such quantity is called parameter of the distribution. The collection of all probability distributions for different values of the parameter is called a family of probability distributions....
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This note was uploaded on 09/27/2010 for the course STAT 104157 taught by Professor Jhonbran during the Spring '09 term at California Coast University.
 Spring '09
 JHONBRAN

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