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Math Help - Compute Probabilities by Conditioning

  1. #1
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    Compute Probabilities by Conditioning

    Hi,

    I would like to know if someone is able to help me in the following question:


    A total of 11 people, including you, are invited to a party. The times at which people arrive at the party are independent uniform (0,1) random variables.


    a) Find the expected number of people who arrive before you.
    b) Find the variance of the number of people who arrive before you.

    ___
    I have tried the following:
    Let X be the number of people arriving before me
    Let T be my arrival time

    E[X] = integral of (E[X/Y=y]fy(y) dy

    After I am not too sure..
    Can someone please help me.

    Thank you very much.
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  2. #2
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    Quote Originally Posted by zxcv View Post
    Hi,

    I would like to know if someone is able to help me in the following question:


    A total of 11 people, including you, are invited to a party. The times at which people arrive at the party are independent uniform (0,1) random variables.


    a) Find the expected number of people who arrive before you.
    b) Find the variance of the number of people who arrive before you.

    ___
    I have tried the following:
    Let X be the number of people arriving before me
    Let T be my arrival time

    E[X] = integral of (E[X/Y=y]fy(y) dy

    After I am not too sure..
    Can someone please help me.

    Thank you very much.
    Consider your order in the arrivals. It could be 1, 2, 3, ..., 11. By symmetry, all these possibilities are equally likely. So the number of people arriving before you is one of 0, 1, ..., 10, and all these possibilities are equally likely.

    So... maybe you can fill in the rest.

    (Note that we did not need to know the actual distribution of arrival times, even though we were told it is Uniform(0,1). Interesting, eh?)
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  3. #3
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    Joined
    Mar 2009
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    Okay, yeah thanks for the hint, i sort of get the idea.
    Thank you.
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