Stats 309 7-1

# Stats 309 7-1 - 7-1 Random Variables and Probability...

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7-1 Random Variables and Probability Distributions Random variable -a function or rule that assigns a number to each outcome of a random experiment ie – Flip a coin twice S = {HH, HT, TH, TT} Suppose we are interested in the total number of heads that turn up. We let X denote the total number of heads that can turn up. X is a random variable and assigns a numerical value to each simple event in S, with the possible values of X being 0, 1, or 2. X = {0,1,2} There are two types of random variables: Discrete -can assume a countable number of possible values. • We can identify the first value, second value, and all subsequent values. • Countable does not necessarily mean finite. • For example – number of flips until a head appears Continuous -can assume an uncountable number of values. • For example – measurement: time, weight, length

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Discrete Probability Distribution Probability distribution -a table, formula or graph that lists all possible values a random variable can assume along with their associated probabilities. For example: Flip a coin twice X = {0,1,2} P(X=0) = P(TT) = ¼ P(X=1) = P(HT) + P(TH) = ¼ + ¼ = ½ P(X=2) = P(HH) = ¼ X P(X) 0 ¼ 1 ½ 2 ¼
Requirements of a Discrete Probability Distribution If a random variable X can take values x i then, 1)0 ( ) 1 for all 2) ( ) 1 i i i p x x p x p = We can then calculate the probability that X takes a range of values.

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## This note was uploaded on 04/09/2008 for the course MTHSC 309 taught by Professor Cathydavis during the Spring '08 term at Clemson.

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Stats 309 7-1 - 7-1 Random Variables and Probability...

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