Ross Chp. 1-3 Formulas

# Ross Chp. 1-3 Formulas - Thm 3 For a set of n elements take...

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Thm 5: For either ordered or unordered random sampling w/o replacement, the probability that a specific item is included in a sample of size r from a population of size n is r/n. Thm 6: An unordered random sample w/o replacement can be obtained by drawing an ordered random sample w/o replacement and ignoring the order. Thm 3: For a set of n elements, take n1, n2, n3, ... nr such that n1 + n2 + n3 + ... nr = n. It is desired to divide (or partition) the set into r subsets, the first of which has n1 elements, the second

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Unformatted text preview: has n2 elements, . .., and the rth has n r elements. The number of distinct ways in which this can be done is n!/n1!n2!. .nr!). Equivalently: Given n objects, n1 of which are of indistinguishable kind, n2 of which are of a second indistinguishable kind, . .., and nr are of rth indistinguishable kind, then the number of distinguishable permutations of the n objects is exactly n!/(n1!n2!. ..nr!)....
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• Fall '06
• SCHWAGER
• random sample w/o, sample w/o replacement, indistinguishable kind

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