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Math Help - looking 4 some help on Probability theory

  1. #1
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    looking 4 some help on Probability theory

    1) A box contains M disks, numbered from 1 to M. Disks are drawn from the box independently without replacement. What is the probability of the nth disk drawn shows a higher number than any of the previous (n-1) disk?
    Let X_n be a random variable taking value 1 if the nth disk shows a highest number than any of the previous (n-1) disk , and 0 otherwise.

    I have no clue how to do this question. Please help me some guidance how to do it, I mean what kind of distribution model I should use?

    2) Let the sequence X_n = X_1,X_2,....,X_M marks the times at which records( highest observed values) are broken (exceeded)
    Let Y(m,n) be the number of times a record is broken between times m and n ( inclusive). Write down an expression for Y(m,n) in term of the Xs and hence derive and expression for the expected number of records betweem times m and n

    Question 2 is related from part 1. So, in order to do this I think we have to use the result from part 1 but apparently I dont know how to do part 1, so I got stuck on question 2.

    I hope some one could give me some hints.

    Thank you for your time

    KN
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  2. #2
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    Quote Originally Posted by knguyen2005 View Post
    1) A box contains M disks, numbered from 1 to M. Disks are drawn from the box independently without replacement. What is the probability of the nth disk drawn shows a higher number than any of the previous (n-1) disk?
    Let X_n be a random variable taking value 1 if the nth disk shows a highest number than any of the previous (n-1) disk , and 0 otherwise.

    I have no clue how to do this question. Please help me some guidance how to do it, I mean what kind of distribution model I should use?

    2) Let the sequence X_n = X_1,X_2,....,X_M marks the times at which records( highest observed values) are broken (exceeded)
    Let Y(m,n) be the number of times a record is broken between times m and n ( inclusive). Write down an expression for Y(m,n) in term of the Xs and hence derive and expression for the expected number of records betweem times m and n

    Question 2 is related from part 1. So, in order to do this I think we have to use the result from part 1 but apparently I dont know how to do part 1, so I got stuck on question 2.

    I hope some one could give me some hints.

    Thank you for your time

    KN
    1) is easier than it looks.

    Of the n disks drawn, one of them must be the largest so far; and by symmetry, all n disks are equally likely to be that one. So the probability that disk n is the largest seen so far is 1/n.
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  3. #3
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    How can disks be drawn from a box independently without replacement?

    For example, say you have disks numbered 1 through 10. If you first pick disk 4, and you do not replace another (or the same) disk 4 into the box, then your chances of drawing a 7, for example, has gone from 1/10 to 1/9. Therefore, we have a dependent relationship.

    -Andy
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