Chapter 3a

# Chapter 3a - 1 PROBABILITY DISTRIBUTIONS RANDOM VARIABLES...

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PROBABILITY DISTRIBUTIONS RANDOM VARIABLES Random Variable: A variable whose numerical value is associated with outcomes in the sample space. Example: Toss two coins. Let the random variable X be the number of tails. S = {HH, HT, TH, TT} Possible values of X: Types of Random Variables: Discrete – countable; whole numbers The number of students in line to buy football tickets. The number of Fridays in a month. Scores for a baseball game. Continuous – not countable; can include fractions/decimals The length of time a student stands in line to buy football tickets. The number of minutes until Friday. Scores for a gymnastics competition. 1

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Probability Distribution of a Discrete Random Variable: The probability distribution is a listing of each potential value of the random variable along with its probability. Each value the discrete random variable can take has a probability associated with it. We write P ( X = x ) to mean the probability that the discrete random variable, X , takes a particular value, little x . If X is a discrete r.v., then f(x) = p(x) = P[X=x] is the density function for X. f(x) is called the probability mass function (pmf). Characteristics of a Discrete Density Function: 1) f(x) > 0 for all x 2) 2 ( ) 1 allx f x =
The probability distribution can be represented by a chart (or table), a graph or a formula. Ex 1) Example of

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## This note was uploaded on 01/17/2011 for the course STAT 4714 at Virginia Tech.

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Chapter 3a - 1 PROBABILITY DISTRIBUTIONS RANDOM VARIABLES...

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