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Unformatted text preview: and its relationship to lambda. MGT 2250 — Lesson 16
Continuous Probability Distributions: The Exponential DiStribution
June 28, 2011 Distribution used to determine the probability of a speciﬁed interval of
time or space between occurrences of an event.
Examples:
1) The time in minutes between arrivals of customers at a
bank teller Window between 11AM and 1PM. I _ 2) The distance between potholes on 100 miles of highway.
Note that these occurrences are measured and that’s Why this is a
continuous probability distribution! Also note that this is a “first cousin” of the Poisson distribution.
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XX ’X “2; e The exponential function: W
m K The exponential prohabilit‘ﬁeurve: Sic/k; The mean%r expected value) of the exponential probability distribution Calcuiating probabiiities for the exponential distribution: Examples:  I) A local bank has determined that the average number of
customers arriving at its drive—in teller windows between the hours of
11 AM and 1PM on week days is 7 per 15 minutes. Assuming these
arrivals follow a Poisson/Exponeﬁﬁ’al distribution: a) What is the probability of an interval between 1 minute and 2
minutes between customer arrivals during those days and hours? /LL patrol/J 7T 7 ?
N” 72%? Cw var N
am“ b) What is the probability ofan interval ofless than 1 minute
between customer arrivals during those davs and, hours? PC K‘EI/ ’“[email protected]
l« £2“) [pew e) What is the probabiiity of an interval of more than 2. minutes
between customer arrivals during those days anti hours? i3( meg) W 21"?) V/EEQ“
eé Lﬂ/ﬂ/ fﬂlggypz 2,2" an»; 2' 7212;” 2) A telemarketing firm has determined that thé aV’ergg Kength of its
calls is 1.5 minutes. Assuming these calls follow a Poisson/Exponential
distribution: a) What is the probability ofa call lasting between 1 minute and 2
minutes? p(:(4;7£27)
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b) Whatis the pro abimyofa call astmg les {bin 1 mitig/M iﬁﬁfjfw z (:7 me“ mm» Péad ? [:6 {A a? in I
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(“K M” 5,45 m.
m. 4w» “MN
47 KW ‘Whai is the probability of a caii iasting more than 2 minutes? ’ ’3 “m r 5%?
“3’25: will 2? JV ‘ a A. ...
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 Summer '08
 Milne
 Normal Distribution, Probability theory, Exponential distribution, probability density function, Exponential Probability Distribution

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