STA6166 F06-9 Random Variables

STA6166 F06-9 Random Variables - Chapter 4 Random Variables...

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Chapter 4: Random Variables Random Variable: A random variable is a variable which takes on a value based on the outcome of a random phenomenon or experiment. We usually denote random variables by capital letters, like X, Y, Z, etc. We denote observed or realized variables with lower case letters, x, y, z, etc. Example 1: Toss 2 fair coins. Let X be the number of heads on the two tosses. Then X is a random variable. Its possible values are 0,1,2. Since there are only a finite number of possible values, X is said to be a discrete random variable. Example 2: Pick a person at random and let Y be the person’s height in inches. Since, in theory, the height could be any real number up to 80 inches or so, Y is said to be a continuous random variable. Probability Distributions : In Example 1, we could list the possible values of X and their probabilities. This is called the probability distribution or probability model for X. To get the distribution of X, we first list the outcomes of the experiment: Outcome Probability X HH ¼ 2 HT ¼ 1 TH ¼ 1 TT ¼ 0 Therefore, the probability distribution of X is Number of heads x Probability P(X = x ) 0 1/4 1 1/2 2 1/4 Note that this is still just a model for the distribution of X. The reality of the number of heads on tosses of two coins might deviate from this model (why?), though we might expect the deviation to be small if you did a good job of tossing. Probability distributions can also be represented by probability functions. We will see these later.
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This note was uploaded on 11/23/2011 for the course STA 6166 taught by Professor Staff during the Summer '08 term at University of Florida.

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STA6166 F06-9 Random Variables - Chapter 4 Random Variables...

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