sta4321-8 - Discrete Random Variables Random Variable...

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Unformatted text preview: Discrete Random Variables Random Variable Discrete Random Variable What is a random variable? A random variable is a rigorously defined mathematical construct used to formalize probability. There are three types of random variables: 1 Discrete (Chapter 4) 2 Continuous (Chapter 5) 3 Mixed (Discrete + Continuous) (End of Chapter 5) Definition (formal definition of random variable) A random variable is mapping of the sample space to the real numbers. Example (coin toss) A coin toss can be characterized by the following random variable: X = 1 , if heads , if tails . Arthur Berg Discrete Random Variables 2/ 9 Random Variable Discrete Random Variable What is a random variable? A random variable is a rigorously defined mathematical construct used to formalize probability. There are three types of random variables: 1 Discrete (Chapter 4) 2 Continuous (Chapter 5) 3 Mixed (Discrete + Continuous) (End of Chapter 5) Definition (formal definition of random variable) A random variable is mapping of the sample space to the real numbers. Example (coin toss) A coin toss can be characterized by the following random variable: X = 1 , if heads , if tails . Arthur Berg Discrete Random Variables 2/ 9 Random Variable Discrete Random Variable What is a random variable? A random variable is a rigorously defined mathematical construct used to formalize probability. There are three types of random variables: 1 Discrete (Chapter 4) 2 Continuous (Chapter 5) 3 Mixed (Discrete + Continuous) (End of Chapter 5) Definition (formal definition of random variable) A random variable is mapping of the sample space to the real numbers. Example (coin toss) A coin toss can be characterized by the following random variable: X = 1 , if heads , if tails . Arthur Berg Discrete Random Variables 2/ 9 Random Variable Discrete Random Variable What is a random variable? A random variable is a rigorously defined mathematical construct used to formalize probability. There are three types of random variables: 1 Discrete (Chapter 4) 2 Continuous (Chapter 5) 3 Mixed (Discrete + Continuous) (End of Chapter 5) Definition (formal definition of random variable) A random variable is mapping of the sample space to the real numbers. Example (coin toss) A coin toss can be characterized by the following random variable: X = 1 , if heads , if tails . Arthur Berg Discrete Random Variables 2/ 9 Random Variable Discrete Random Variable Probability Mass Function Definition (discrete random variable) A random variable X is said to be a discrete random variable if it takes on a finite or countably infinite number of possible values. (Note: A set is said to be countably infinite if it can be mapped bijectively to the integers.) Definition (probability mass function) Every discrete random variable has an associated probability mass function (pmf), p ( x ) , that assigns a probability to each possible value x ....
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sta4321-8 - Discrete Random Variables Random Variable...

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