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xEnOnn

  • 2 years ago

There are 25 students at a bus stop. It is known that on average, 3 buses arrive at the bus stop in every 20 minutes. What is the probability that the waiting time for the next bus is at least 30 minutes? State the assumptions you need to compute the above probabilities.

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  1. xEnOnn
    • 2 years ago
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    I believe it has got to do with Poisson distribution but I am not sure how to start from it. :(

  2. xEnOnn
    • 2 years ago
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    So the number of buses has become the interval instead? But isn't time the only unit for the interval in poisson?

  3. xEnOnn
    • 2 years ago
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    Also, the question asked for the assumptions that were made in computing the probabilities. What assumptions have we made in this calculation? I don't understand what kind of assumptions have we made.

  4. Tributized
    • 2 years ago
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    nice prof pic lol..

  5. xEnOnn
    • 2 years ago
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    Also, to have X~Pois(20/3), and find P(X>=30)=1-P(X<30), The P(X<30) is very close to 1. This would make P(X>=30)=1-1=0, which looks weird.

  6. Zarkon
    • 2 years ago
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    wouldn't it be Poisson\(\displaystyle\left(\frac{3}{20}\cdot 30\right)\)=Poisson(4.5)

  7. Zarkon
    • 2 years ago
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    Calculate P(X=0)

  8. xEnOnn
    • 2 years ago
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    Why calculate the probability of X=0?

  9. Zarkon
    • 2 years ago
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    0 buses arriving in the first 30 mins

  10. xEnOnn
    • 2 years ago
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    OHH!!! wow!! This is smart!

  11. Zarkon
    • 2 years ago
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    time to teach..be back later

  12. xEnOnn
    • 2 years ago
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    wow! this feels counter intuitive but somewhat logical. i wouldn't have thought of it. It's like so there is zero buses during the first 30mins and so this probability is as good as there is at least a bus after this first 30mins. thanks!!

  13. xEnOnn
    • 2 years ago
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    ok sure! Thanks for you help!!!

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