ch-3-3502 - CHAPTER 3 Random Variable A rule that associate...

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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 tune-ups knows that 45% of all tune- ups are done on four cylinder automobiles, 40% on six cylinder automobiles, and 15% on eight-cylinder 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.

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ch-3-3502 - CHAPTER 3 Random Variable A rule that associate...

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