stat3021-ch3-Sol.pdf

# stat3021-ch3-Sol.pdf - STAT 3021 Chapter 3 Random variables...

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STAT 3021 Chapter 3. Random variables and probability distributions 3.1 Concept of a random variable In an experiment that can have more than one possible outcome, we use random variable to describe outcomes numerically. For example, when we flip a fair coin three times, all possible outcome may be written S = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT } where T = tail, H= head. Let X be the random variable that represents the number of heads. Then X = 0 , 1 , 2 , or 3 . Outcome x P ( X = x ) P ( X x ) TTT x = 0 P ( X = 0) = 1 8 P ( X x ) = 1 8 TTH, HTT, THT 1 3 8 4 8 HHT, HTH, THH 2 3 8 7 8 HHH 3 1 8 1 Definition 3.1 Note: We denote a random variable by a capital letter , such as X . We denote values of variables by lower case letters, such as x or x 1 . Notation P ( X = x ) represents the probability that random variable X is equal to a particular value x . For instance, P ( X = 1) refers the probability that a random variable X is equal to 1. Example 1. (Example 3.3 in page 82) Consider the simple condition in which components are arriving from the product line and they are stipulated to be defective or not defective. Define the random variable X by X = ( 1 , if the component is defective , 0 , if the component is not defective . 1

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STAT 3021 As in Example 1 if there are only 2 categories for a variable and you are interested in one category, Bernoulli random variable , X , takes 1 for the category of interest and 0 for the other category. 2
STAT 3021 Definition 3.2 A random variable is called a discrete random variable if its set of possible outcome is countable. A Bernoulli random variable is the simplest discrete random variable.

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• Fall '08
• Staff
• Statistics, Probability, Probability distribution, Probability theory, probability density function, Discrete probability distribution

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