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Surface density of random variable

(1 ,(=,(,) no concept of the joint distribution of density, but by their surface density (, y,, (, y)) obtained (, () and (, () the edge density. with a parallel to the 0 = and perpendicular to the O = surface plane clusters to cut O = surface, will be. = surface into many small form AD, AD \O, at the same time, the plane will also be = one cluster, 【y) is divided into many small patches, for any one of a small rectangle AD, in small patches on ==,(,) d, d:, d, 'stare. , d corresponding, so the following theorem. Theorem 3: Let ((,) a (, y), three-dimensional random variable (,[link widoczny dla zalogowanych],,() satisfies (;,(, 1), if == f (x, ) is defined in ((,) to take on the range with first-order continuous partial derivatives of functions,[link widoczny dla zalogowanych], then ((,) the joint distribution density: 』('= heat of the Po √ 1 + g: + g,:,, ...) l = where:;.,[link widoczny dla zalogowanych], on the grounds = f (x, y) determined, = as the independent variables. as the dependent variable of the inverse function of i-branch. Proof: For any small rectangle △ D, -.. Pf (, ~) 6AD} = Pf (, (, 1) Ed} i; 1,2, ..., 『』 (, z) Kdxdz = 『jΣ (, (, z) z) da △ D. r-Ifj (,(,=)=, f-::-:'。:_ dd = △ D. (turn 7 Cool

78 - Shandong Institute of Engineering l998 years AbstractAccordingtotheexperienceoftheauthorinadmanistrationoftechnologicalcontract, thispaperanalysessomepointst.owhichatt ~ ntioashouldbcpaidandsomeproblemScausedbynon-standardizationoftechnologicalCOntractandgivessomesuggestionsforavoidingdisputesdevelopedincarryingouttheCOntractKeywordsTechno10gica1contract, Signation, Carryingout ( on the next page), d ~ = J = Ao plus Die with any of the ..., l = bite,) '2 with friends Huang】 ..., l where :=(,,) as z = f (x,) as the independent variables on the dependent variable number of anti-shad., O, z), (z) as = (, z) respectively on with: the partial derivative of the probability of reference l,[link widoczny dla zalogowanych], Fudan University, Beijing: People's Education Press ,】 9792 Yanshi Jian, Wang Jun, Xiang, Liu Xiufang probability theory Beijing Science Press,[link widoczny dla zalogowanych], l985CurvedSurfaceDistributionDensityofStochasticVariablesLf0/og (Shanx [WeinanTeachersCollege) AbstractThispaperdealswithprobabilitydistributonoftridimensionalstochasticvaviablesofcontinUPUStype (,, f) = f (,), introducingthedefinitonofcurvedsurfacedistributiondensityandderivinganalysisexpressionswithdesityfunctionof (andedgedensityof (,),(,() given . Thepaperalsodiscussedtheappicationcfdensityformulaof (withexampiesKeywordsStochasticvaviables, Curvedsurfacedistributiondensity, Unitedistribu ・ tiondensity, Curvedgutfaceintegration

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