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Unformatted text preview: Chapter 3 Random Variables and Probability Distributions 3.1 Random Variables Definition 3.1 A random variable ( r.v. ) is a real-valued function defined on the sample space. • There are mainly two types of random variables: discrete : taking finite or countably infinite possible values continuous : taking all possible values in an interval Example 3.1 Two balls are randomly chosen ( without replacement ) from an urn containing 2 white and 3 black balls. Let X be the number of white balls selected. Then X is a r.v. taking on values , 1 , 2 with Example 3.2 Select 3 balls from an urn contains 20 balls numbered 1 through 20 . If you bet $ 10 that at least one of the drawn balls has a number ≥ 17 , what is the probability that you win $ 10 ? 3-1 Solution : Example 3.3 Toss a coin 4 times. Assume P ( Heads ) = 2 / 3 . Let X be the number of heads. Then X is a random variable with P ( X = k ) = for k = 0 , 1 , 2 , 3 , 4 ....
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