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Probability densities

by mikemike123
Tags: densities, probability
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mikemike123
#1
Dec13-09, 06:25 PM
P: 5
Heres the question.... The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.

The question I am stuck on is....

Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes. (The first part of the problem was to find probability you wait longer then an hour which I figured the limits would be (60<x<infinity).

Well i know mew=beta=10 min=1/lambda=1/10

f(x)= lambda*e^-lambda which will ultimately give me 1/10e^-1/10xdx. I have my integral set up, the thing is I cant figure out my limits. My initial guess was to evaluate the integral from (0<x<60) and subtract (70<x<infinity), ultimately giving me the answer .9984 or 99.84%. I thought it was right but apparently wrong, can someone please help me set up the appropriate limits. Thanks in advance.
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sylas
#2
Dec13-09, 07:06 PM
Sci Advisor
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P: 1,750
Quote Quote by mikemike123 View Post
Heres the question.... The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.

The question I am stuck on is....

Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes. (The first part of the problem was to find probability you wait longer then an hour which I figured the limits would be (60<x<infinity).

Well i know mew=beta=10 min=1/lambda=1/10

f(x)= lambda*e^-lambda which will ultimately give me 1/10e^-1/10xdx. I have my integral set up, the thing is I cant figure out my limits. My initial guess was to evaluate the integral from (0<x<60) and subtract (70<x<infinity), ultimately giving me the answer .9984 or 99.84%. I thought it was right but apparently wrong, can someone please help me set up the appropriate limits. Thanks in advance.
Not subtract. You have a conditional probability here.
mikemike123
#3
Dec13-09, 07:19 PM
P: 5
Ok so if my given is the answer I got for my first part, .0025. How would I go on finding the Probability of P(AintersectB)?

sylas
#4
Dec13-09, 07:41 PM
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P: 1,750
Probability densities

Quote Quote by mikemike123 View Post
Ok so if my given is the answer I got for my first part, .0025. How would I go on finding the Probability of P(AintersectB)?
You need Pr(60 < t < 70) given Pr(60 < t). What's the formula for that?


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