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Random Variables November 23, 2009 Discrete Random Variables • A random variable is a variable whose value is a numerical outcome of a random phenomenon. • When each value of a random variable can be assigned a probability, the random variable is discrete. Probability Distributions • This list of probabilities assigned to each possible value of a random variable X is called the probability distribution of X. • The probability distribution can be written as a table, or as a histogram (called a probability histogram). • In order to be a legitimate probability distribution, the probabilities must fall between 0 and 1 and sum to 1. Example 1 (Uniform Distribution) • Imagine picking a digit from the (infinite) decimal expansion for . Let X be the random variable whose value is the digit you pick. The probability for each digit is equally likely. • Find the probability distribution and make a probability histogram. What is P(X > 3)? Example 2 • Spell-checking catches “nonword errors,” which result in a string of letters that is not a word (such as “teh” for “the”). • Let X represent the number of nonword errors in a 250 word essay. • The variable X has the following probability distribution: errors 0 Prob. 0.1 1 0.2 2 0.3 3 0.3 4 0.1 Example 2 Continued • Verify that this gives a legitimate probability distribution. • Write the event “at least one nonword error” in terms of X. What is the probability of this event? • Describe the event X ≤ 2 in words. What is the probability that X < 2? Assignment • • • • Page 461: 7.2,7.3 and 7.4 Page 475: 7.7 and 7.8 Page 477: 7.12,7.14,7.15 and 7.20 Due Wednesday