By Charles J.(Charles J. Stone) Stone

ISBN-10: 0534233287

ISBN-13: 9780534233280

This author's glossy procedure is meant basically for graduate-level mathematical facts or statistical inference classes. the writer takes a finite-dimensional useful modeling perspective (in distinction to the traditional parametric technique) to bolster the relationship among statistical concept and statistical technique.

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Extra info for A Course in Probability and Statistics

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The number of operations should be of order n. Solution. Assume all numbers that can be represented as sums of subsets of {a[1] . . . a [ k ] } form the set {1,2 . . . N}. If a [ k + l ] > N+I, then N+I is the smallest number that cannot be represented as the sum of some subset of {a[1] . . . a [ n ] }. If a [ k + l ] _< N+I, then all numbers that can be represented as sums of subsets of {a [ 1] ... a [k+ 1] } form the set {1, 2 . . . N+a [k+ 1] }. 2 Arrays 27 k := O; N := O; { i n v a r i a n t relation: all the numbers that can be r e p r e s e n t e d as sums of subsets of {a[l] ....

8. The same problem where all elements are integers in 1 . k and the number of operations should be of order n + k. 9. L. ) A rectangular field m x n contains mn squares. Some squares are marked as black. It is known that black squares are grouped into several disjoint rectangles that are at least one apart from each other. The number of operationsshould be of orderran. Solution. The number of rectangles is equal to the number of their upper left comers. It is easy to check whether a square is in the upper left comer.

Find this number (or one of them, if there is more than one). The number of operations should be of order p + q + r . Solution. pi:=i; ql=l; r1:=1; {invariant relation: x [ p l J . 24. Repeat the previous problem assuming that we do not know in advance if such a common element exist. Determine whether or not it exists and locate it if it does. 25. The array a [ 1 . n] consists of arrays [ 1 . m] of integer; a [ 1 ] [1] < . - - < a [ 1 ] [m] . . . a [ n ] [1] < . - . < a [ n ] [m]. It is known that there is a common number present in all a [ i ] (that is, there exists an x such that for all i in 1 .

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A Course in Probability and Statistics by Charles J.(Charles J. Stone) Stone


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