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discrete r.v.s - Chapter 5 Discrete Random Variables and...

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Chapter 5: Discrete Random Variables and Their Distributions Four of the most important discrete random variables: Binomial, Hypergeometric, Poisson, and Geometric Variable - denotes a characteristic that varies from one person or thing to another Ex: height, weight, marital status, gender, eye color, education level attained, etc. Variables can be either quantitative (numerical) or qualitative, sometimes called categorical (descriptive variable) Example: The following is a chart describing the number of siblings each student in a particular class has (there are 40 students total). Siblings x Frequency Of Students Relative Frequency Percentage Of Students 0 8 .200 20.0 1 17 .425 42.5 2 11 .275 27.5 3 3 .075 7.5 4 1 .025 2.5 40 1.000 100.0 Definition 5.1: Random Variable A random variable is a real-valued function whose domain is the sample space of a random experiment. In other words, a random variables is a function : X R Ω → where is the sample space of the random experiment under consideration, and R represents the set of all real numbers. (You can think of a random variable as a way of assigning probabilities to an event of an experiment.) Ω Important other examples of a random variable: the amount of an insurance claim and the lifetime of a flashlight battery.
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