homework help > math > statistics and probability q&a board > topic: exponential distribution how to call calculat...

Q BgQuestion:

      
Pupil
Karma Points: 50
Respect (100%):
posted by  rocky888 on 11/5/2009 2:24:20 AM  |  status: Closed  |  Earned Karma: 50

Exponential Distribution how to call calculate F(X)

Course Textbook Chapter Problem Needs by
Statistics and Probability A First Course in Probability (6th) by Ross 5 Example 5.b 11/5/2009 at 11:00:00 AM
Question Details:
Hi i was wondering if someone could explain the following as referred to in red, many thanks:

Example 5b. Suppose that the length of a phone call in minutes is an exponential random variable with parameter λ = 1/10. If someone arrives immediately ahead of you at a public telephone booth, find the probability that you will have to wait

(a) more than 10 minutes;
(b) between 10 and 20 minutes.

Solution: Letting X denote the length of the call made by the person in the booth, we have that the desired probabilities are:
(a) P { X > 10 } = 1 - F(10) "where is this gotten from"
                         = e^-1 = .368 "how do we get to this line from the previous .i.e. how to work out F(10)"
(b) P { 10 < X < 20 } = F(20) - F(10)
                                  = e^-1 - e^-2 = .233
Bonus Point Alert! Earn +9 additional karma points for helping this platinum member.

AAnswers:

Answer Question Ask for clarification
Guru
Karma Points: 2,564
posted by Orca on 11/5/2009 2:40:07 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
F(x) is the cumulative distribution function.  that is
P(Xx)=F(x)
Since,   
f(x)=λe-λx,    x0
F(x)=
Note
P(X>10)=1-F(10)
P(10<X<20)=F(20)-F(10)
Novice
Karma Points: 42
posted by Anonymous on 11/5/2009 2:50:44 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
There is a formula in which exponential random variable is modelized to depict waiting time at telephone booths .
 f(x) = λe ^ (-λx) . This formula has been used in the question.
To obtain probability of waiting we have a formula :
 P(T>t ) = e^(-λt)  and P(a<=T<b)=e^(-λa)-e^(-λb)
In the question λ=1/10 and t=10 , a=10 , b=20 . Substituting the value the answer has been obtained.
Sak
Answer Question Ask for clarificarion
Ask New Question

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today » How Cramster is different from tutoring »

Need Help In

Useful Links