Let j and n be positive integers with j le n an experiment, Ask an Expert

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Let j and n be positive integers, with j ≤ n. An experiment consists of choosing, at random, a j-tuple of positive integers whose sum is at most n.

(a) Find the size of the sample space. Hint : Consider n indistinguishable balls placed in a row. Place j markers between consecutive pairs of balls, with no two markers between the same pair of balls. (We also allow one of the n markers to be placed at the end of the row of balls.) Show that there is a 1-1 correspondence between the set of possible positions for the markers and the set of j-tuples whose size we are trying to count.

(b) Find the probability that the j-tuple selected contains at least one 1.

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Category:- Statistics and Probability
Reference No.:- M91645030

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