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Math Help - sampling without replacement

  1. #1
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    sampling without replacement

    say i have fifty objects and 1 is the object of interest.With replacement i can modell this as a geometric distribution to find the expectation of the number of bernouli trials required until i pick the object of interest.But if there is no replacemnt then the probabilities change so how do i model this scenario in order to find quantities such as expoectation and variance?
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  2. #2
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    Please be more specific. Are you drawing a sample of fixed size (5 objects, say), or do you have something else in mind like drawing objects until you draw your special object?
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  3. #3
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    i have n marbles. All are white except for one which is blue.If i continually choose one marble at a time without replacement, what is the expectation until i choose the blue?

    I think i have figured it out, because my notes have something on this type of distribution, so i have solved the question, but i still don't fully understand the logic, which is annoying.
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  4. #4
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    Quote Originally Posted by ulysses123 View Post
    i have n marbles. All are white except for one which is blue.If i continually choose one marble at a time without replacement, what is the expectation until i choose the blue?

    I think i have figured it out, because my notes have something on this type of distribution, so i have solved the question, but i still don't fully understand the logic, which is annoying.
    Let X be the random variable of the number of white marbles chosen before a blue marble is chosen.

    Draw a tree diagram to an extend where it's sufficient for you to see a pattern.

    P(X=0)=1/n

    P(X=1)=((n-1)/n) x 1/(n-1) =1/n

    P(X=2)= ((n-1)/n) x ((n-2)/(n-1)) x (1/(n-2)) = 1/n

    ...

    P(X=n-1)=1/n

    E(X)=0+1/n+2/n+3/n+...+(n-1)/n

    and the sum of this AP is (n-1)/2

    so if you have 50 marbles, you are expected to pick (50-1)/2 white marbles before the blue marble is picked.
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