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A Class of Integral Problem

ticmethodisusedtosolveakindofintegralproblem. Itnoton1ylinksupthedifferentcourseutalsosimplifiestheproofandtheoperations. Keywords: multipleintegral; randomvariable Lemma []: Let 7 be any random variable,[link widoczny dla zalogowanych], E (knock) exists,[link widoczny dla zalogowanych], there are E (7) J0P (7 ≥ y) d3,[link widoczny dla zalogowanych], a jnP (7 <A y) dy theorem [] factories (z) is a dollar Bore1 measurable function, then E (f ()) = If (x) dFr (z) 1 find the following triple integral main results: (1) Find the integral solution: a mathematical analysis of the subject method more cumbersome. Here are the problem-solving methods of probability theory, by comparison, has become more simple and clear. Stochastic model constructed as follows: Let (12 ...,) is from the mother of the simple random sub-sample, independent of each other, and are subject to U 【a, b], (z1, z2 ..., z) to its observed value, F (z ) is the parent of the distribution function, then (1, ...,) the joint probability density function P (Xl, X2 ..., z) = j, mouth ≤ z ≤ =- '2 '..., 【0, the other in mind a = min {1,2, ...,}, then there is E (a) = E (min {1,2, ...,}) = j A ... j a min {z1, ..., z} (., ...,) dz1 ... dz: ... min {z, ..., z} dz ... dz On the other hand, seek Received :2003-10-08. Fund: 2003 School Youth Fund funded project number 2OO3Q19. -Hr, author: Liu Ruijuan (1977 a), female, Jiangsu Pei County, MS, research methods. To the functional analysis. a ≤, z7 ≤ b, nXd2zdzdz2zzm =,, 0 z ~ 6 the value of E, one by one he was 6 its a Liurui Juan: a Class of Integral Problem 41 * So r +. . E (a) = Ip (z) dx = √ a oaz (an d work = high (6d workers prepared = = 6, it was J ... Jmin {z, ...,,} ddz: ... dz = (6 a lE ( a) = (6 I (2) Find the value of integral jmax ... .... Solution: structure similar to the above model, where l, 2 ... independent of each other, and are subject to U [a, b], then (, 2 ...,) is joint probability density function (zl, z2 ..., z,) = j, n ≤ z ≤ = ... l0, the other in mind Lu = max {, 2, ...,}, beta 4 with E (Lo) = E (max { , 2, ...,}) = J ... Jmax {xl,, ..., z ,}(..,) dzl ... dz, = chi maxXl, X2, '\≤ 6, l0, the other so r +.. E (Lo) = I.. Lo (z) dx = (A dz = Chi fb (z-nn-1dz = 6 \{zzz, ..., z} dxdzz ... dz, = (6 A n) E (a) = (6 a n), z emperor - the title for the quadrature, the probability of thinking can prove the following: the use of probability theory Function of mathematical expectation, to construct a probability distribution for the uniform distribution of the random model, constructed with the integrated function of great samples, minimum order statistics, whereas the conversion of the quadrature value to the maximum or minimum for the sake of mathematical expectation of order statistics of probability theory 2 the conclusion of the ideology, not difficult to calculate the value of the following points: (1) Find the integral ... jmin {,, ...,} ..., where n: t0 ≤ z ≤ 1, i = 1,2, ...,} (2) Find the integral ... J. A {z, z, ..., z} ... dz where n = t0 ≤ V ≤ 1, i = 1,2, ...,} References: [1 ] Rohat ~ VK.AnIntmdtmiontoPmlM ~ tyTheoryandMattmmticEStatistics [J]. NewYork: JohnWtley & Sons, 1976, (154) :78-92. [2] weeks of almost content. Probability and Mathematical Statistics [M]. Higher Education Press, 1984. [3] Dai Zhaoshou. a kind of inequality in the probability proof of [J]. Qufu Normal University, 1985, (2): 51. [4] Dai Chaoshou. random variable on the median of its first moment [J]. Xuzhou Normal University, 2002, (4): 4.

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