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Math Help - probability with independant variables

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by qwerty321 View Post
    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.
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  3. #3
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    Does independence imply that all three can be serviced simultaneously?

    Maybe they have to wait for each other?

    Just thinking out loud.
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  4. #4
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    Quote Originally Posted by TKHunny View Post
    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.
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