# Thread: probability with independant variables

1. ## 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

2. 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.

3. Does independence imply that all three can be serviced simultaneously?

Maybe they have to wait for each other?

Just thinking out loud.

4. 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.