# probability with independant variables

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• Jan 20th 2010, 11:19 AM
qwerty321
probability with independant variables
hello i need help:

A doorman is trying to get three taxicabs for three different couples. The arrivals of empty cabs has an exponential distribution with mean 2 minutes. assuming independance, what is the probability that he will get al three couples taken care of within six minutes.

in the book the answer is:0.5678
what i did is sum the three independant variables and i got a gamma distribution with mean 2 and alfa=3 then i calculated the integral from 0 to 6 but the answer is wrong

thanks for the help
• Jan 20th 2010, 01:44 PM
awkward
Quote:

Originally Posted by qwerty321
hello i need help:

A doorman is trying to get three taxicabs for three different couples. The arrivals of empty cabs has an exponential distribution with mean 2 minutes. assuming independance, what is the probability that he will get al three couples taken care of within six minutes.

in the book the answer is:0.5678
what i did is sum the three independant variables and i got a gamma distribution with mean 2 and alfa=3 then i calculated the integral from 0 to 6 but the answer is wrong

thanks for the help

Hi qwerty,

The relevant question is not whether the sum of the the arrival times is less than 6 minutes but rather whether the maximum of the three arrival times is less than 6 minutes.
• Jan 20th 2010, 01:53 PM
TKHunny
Does independence imply that all three can be serviced simultaneously?

Maybe they have to wait for each other?

Just thinking out loud.
• Jan 21st 2010, 02:09 PM
awkward
Quote:

Originally Posted by TKHunny
Does independence imply that all three can be serviced simultaneously?

Maybe they have to wait for each other?

Just thinking out loud.

I suppose independence implies the taxis don't need to wait on each other.