STA 301 - Ch 03 - pp 45-54

STA 301 - Ch 03 - pp 45-54 - Chapter 3: Random Variables...

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Chapter 3: Random Variables and Probability Distributions 45 CHAPTER 3 — RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS A random variable is a function that associates a real number with each element of a sample space. A random variable is generally denoted by a capital letter: X, Y, etc. An observed value of a random variable is denoted by a lowercase letter: x, y, etc. Example: Suppose a coin is flipped 3 times. The sample space is for this experiment is { } TTT HTT THT TTH THH HTH HHT HHH S , , , , , , , = . Letting X be the random variable describing the number of heads observed, we obtain: Sample Space Elements x HHH 3 HHT, HTH, THH 2 HTT, THT, TTH 1 TTT 0 Example : Suppose an individual plays the lottery each week until he wins the jackpot (and then he stops). Letting W represent the event that the individual wins the lottery, and letting L represent the event that the individual does not win, our sample space is: { } K , , , , , LLLLW LLLW LLW LW W S = We may construct a random variable, X , to indicate the number of weeks it takes the individual to win the lottery: Sample Space Elements x W 1 LW 2 LLW 3 LLLW 4 LLLLW 5 M M In each of the above examples, the set of possible values of X is discrete. Such random variables are called discrete random variables .
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Chapter 3: Random Variables and Probability Distributions 46 Random variables with an uncountable number of possible values are called continuous random variables . Example : Doug arrives at his bus stop and records the time (in minutes) until his bus arrives. Let X be the random variable representing this time. The sample space is
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STA 301 - Ch 03 - pp 45-54 - Chapter 3: Random Variables...

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