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Mathematical Gems III by Ross Honsberger

By Ross Honsberger

Ross Honsberger is the writer of six books released within the Dolciani Mathematical Expositions sequence, each one of which provides difficulties from algebra, mathematics, quantity concept, chance, and geometry, and gives us with an creative strategy to these difficulties. His most modern addition to the Dolciani sequence is: "More Mathematical Morsels" that is a continuation of the sooner "Mathematical Morsels" quantity released in 1979. the issues awarded listed below are intended to be loved, instead of coach, even if guideline is nearly constantly the automated derivative. the entire difficulties during this assortment are involved basically with easy difficulties, yet every one of them comprises anything fascinating - a stunning consequence, an interesting technique, a stroke of ingenuity.

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ARNOLD, P. , PROSCHAN, F. and TONG, Y. L. (1988). Crossing properties of mixture distributions. Technical Report M-796, Department of Statistics, Florida State University, Tallahassee. BOLAND, H. A. and GROENEVELD, R. A. (1982). Measures of local variation in a distribution: expected length of spacings and variances of order statistics. Biometrika 69, 227-232. DAVID, J. (1976). The effect of transformations on Lorenz curves. Econometrica 44, 823-824. FELLMAN, J. L. (1971). A general definition of the Lorenz curve.

3. Let g : IR —• R . The following are equivalent, r (i) g(X)

V) P(f(X)

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