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W5-slides1

# W5-slides1 - Lecture 14 Outline and Examples Continuous...

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Lecture 14- Outline and Examples Continuous random variables (Ross Ch 5) -Deﬁnition (Ross § 5.1) -Expected value and variance(Ross § 5.2) -Uniform random varibale (Ross § 5.3)

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Probability density functions Example Experience has shown that while walking in a certain park, the time X , in minutes, between seeing two people smoking has a density function of the form f ( x ) = ( λ xe - x x > 0 0 otherwise. (a) Calculate the value of λ . (b) Find the probability distribution function of X . (c) What is the probability that Jeﬀ, who has just seen a person smoking, will see another person smoking in 2 to 5 minutes? In at least 7 minutes?
Expected value and Variance For discrete random variable X E [ X ] = X x xP ( X = x ) . The analogous deﬁnition when X is a continuous r.v. with p.d.f. f X is E [ X ] = R -∞ xf X ( x ) dx . As in the discrete case E [ g ( X )] = R -∞ g ( x ) f X ( x ) dx .

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Variance Var ( X ) = E [( X - μ ) 2 ] where μ = E [ X ]. Alternately, this can be written as Var ( X ) = E [ X 2 ] - ( E [ X ]) 2 .
Uniform random variables

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W5-slides1 - Lecture 14 Outline and Examples Continuous...

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