L16Exponential

# L16Exponential - and its relationship to lambda MGT...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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. ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

L16Exponential - and its relationship to lambda MGT...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online