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Random Variables

# Random Variables - Random Variables and Probability...

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Random Variables and Probability Distributions

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Which wager would you prefer? You are given \$100 and must pick one of two wagers, for an outcome based on flipping a fair coin: a) You win \$200 if it comes up heads and lose \$50 if it comes up tails b) You win \$350 if it comes up heads and lose your original \$100 if it comes up tails.
Random Variables 1. Numerical measurement of the outcome of a random phenomena.(Agresti) 2. A variable that has a single value, determined by chance, for each outcome of a procedure.(Triola) 3. A numeric function that assigns probabilities to different events in a sample space. A function whose domain is a sample space and whose range is a set of real numbers. (Goldberg)

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Random Variables Give a probability space, , a random variable X is a class of measurable functions, that is an element of, where Ω is the sample space, is the of subsets of Ω and ( 29 0 , P L A ( 29 , , A P A σ-algebra ( 29 1 P Ω =
Random Variables Discrete Countable number of outcomes Continuous Uncountable number of outcomes

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Random Variables a. The cost of making a randomly selected movie b. The number of movies currently being shown in U.S. theaters c. The exact running time of a randomly selected movie d. the number of actors appearing in a randomly selected movie e. The weight of the lead actor in a randomly selected movie
Probability Distributions A graph, table or formula that gives the

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Random Variables - Random Variables and Probability...

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