Lecture17_Chapter4

# Lecture17_Chapter4 - Lecture 17 Chapter 4 Wednesday October...

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Lecture 17 – Chapter 4 Wednesday, October 22 nd

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Continuous random variable ± In Chapter 3 we have seen that a continuous random variable is one that can take any possible value in a given interval. ± Example: ² People weight ² People height ² Distance between two cities
Probability Distribution ± Now if X is continuous random variable the probability distribution or probability density function (pdf) of X is a function f(x) such that () ( ) b a P aXb f x d x ≤≤=

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Legitimate pdf ± A function f(x) is a legitimate pdf, if it satisfies the following two conditions: ² ² ( ) 0 f xx ≥∀ () 1 f xd x −∞ =
Important note ± Note that in the continuous case P(X=c)=0 for every possible value of c. (why?) ± This has a very useful consequence in the continuous case: ( ) ( ) ( ) ( ) P aXb P P P ≤= <≤= ≤<= <<

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Example 4.5 page 158
Uniform distribution ± A continuous random variable X is said to have a uniform distribution on the interval [A,B] if the pdf of X is the following: () 1 , 0, AxB fx BA otherwise ≤≤ =

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## This note was uploaded on 09/23/2009 for the course STAT 318 taught by Professor Staff during the Fall '08 term at Penn State.

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Lecture17_Chapter4 - Lecture 17 Chapter 4 Wednesday October...

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