L16Exponential

L16Exponential - and its relationship to lambda MGT...

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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. .K. "' - 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) ,immis * w (a, “(it )mvg w ) /” N? , .xfi y .“r‘ wig/f? Q'QWq/i} b) Whatis the pro abimyofa call astmg les {bin 1 mitig/M ifififjfw z (:7 me“ mm» Péad ? [:6 {A a? in I \. (“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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L16Exponential - and its relationship to lambda MGT...

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