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1.
随机向量的函数的独立性的一个问题 总被引:7,自引:2,他引:5
给出了随机变量X1,X2,X3,X4每三个相互独立,但X1&;#177;X2与X3&;#177;X4不相互独立的例子,以及X1,X2,X3每两个相互独立,但X1&;#177;X2与X3不相互独立的例子。 相似文献
2.
A组一、选择题 (每小题 3分 ,共 3 0分 )1 . ( - 2 ) 2 平方根是 ( ) .A . - 1 .4 2 B .± 1 .4 2C . - 2 D .± 22 .下列各式求值正确的是 ( ) .A . 3 2 =± 3 B .± ( - 4) 2 =± 4C . - ( - 4) 2 =4D . ( - 3 ) 2 =- 33 .使式子 -x2 有意义的x是 ( ) .A .全体正数 B .全体负数C .零D .非零数4 .一个自然数的算术平方根是x ,则下一个自然数的算术平方根是 ( ) .A .x + 1 B .x2 + 1C .x + 1D .x2 + 15. 1的 2n(n为任意正整数 )次方根为 ( ) .A . 1 B . - 1 … 相似文献
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选择题 (本大题共 14小题 ;第 1~ 10题每小题 4分 ,第 11~ 14题每小题 5分 ,共 6 0分 .在每小题给出的四个选项中 ,只有一项是符合题目要求的 )1 已知全集I =R ,集合M ={x||x - 1|<2 } ,集合N ={x|x 1<2 } ,则 ( )(A)M =N . (B)M N .(C) M∩N ={ - 1} .(D)M∩ N ={ - 1} .2 双曲线 3x2 - y2 =- 3的渐近线的方程是 ( )(A) y =± 3x . (B) y =± 13x .(C) y =± 3x . (D) y =± 33x .3 若 3sinθ =cosθ ,则cos2 θ 12 sin2θ的值是 ( )(A) 65. (B) - 65.(C)… 相似文献
6.
设X=■为球对称分布的矩阵,本文将证实如下命题的等价性:1.X_(1)与X_(2)相互独立;2.X′_(1)X_(1)与X′_(2)X_(2)相互独立;3.vec X依 N(0,V■I)分布,V是某个非负定阵。最后,在P(X=0)<1条件下,我们将关于二次型的Cochran定理推广至更一般的情形。 相似文献
7.
设k是一个正整数,G是一个顶点数为|G|=4k的图. 假设σ\-2(G)≥4k-1, 则G有一个支撑子图含k-1个4圈和一条顶点数为4的路,使得所有这些圈和路都是相互独立的. 设G=(V\-1,V \-2;E)是一个二分图使得|V\-1|=|V\-2|=2k. 如果对G中每一对满足x∈V\-1和y∈V\-2的不 相邻的顶点x和y 都有d(x)+d(y)≥2k+1, 则G包含k-1个相互独立的4圈和一条顶点数为4的路,使得所有这些圈和路都是相互独立的,并且此度条件是最好的. 相似文献
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同步内容 :复数的概念 ,复数的运算 ,坐标变换 .选择题 (共 14个小题 ,第 1— 10题每小题 4分 ,第 11— 14题每小题 5分 ,共 6 0分 )1 如果用C ,R ,I分别表示复数集、实数集和纯虚数集 ,其中C为全集 ,那么有 ( )(A)C =R∪I . (B)R∩I ={0 }.(C)R∩I = . (D)R =C∩I .2 下面四个式子中 ,正确的是 ( )(A) 3i>2i. (B) | 2 3i| >| 1- 4i| .(C) | 2 -i| >2i4. (D)i2 >-i .3 z与1-z22 是两个共轭虚数 ,则z是 ( )(A) 1 2i. (B) 1± 2i.(C) - 1 2 i . (D) - 1±… 相似文献
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A组题一、判断题 (每小题 2分 ,共 1 0分 )1 .x5-y5=(x2 -y2 ) (x3 +y3 ) ( ) .2 .(x -y) n=(y-x) n(n为偶数 ) ( ) .3 .x6-y6=(x3 -y3 ) (x3 +y3 )=(x -y) (x2 +y2 ) (x3 +y3 ) ( ) .4.(a -b) 2 -(a +b) 2 =2a4( ) .5 .8a3 -6a2 +2a的公因式是 2a ( ) .二、选择题 (每小题 3分 ,共 2 4分 )1 .1 6a2 +2m +b2 是一个完全平方式 ,那么m的值是 ( ) .A .± 4ab B .± 1 6ab C .± 3 2ab D .1 6ab2 .下列分解因式错误的是 ( ) .A .4a2 -1 =( 2a +1 ) ( 2a -1 )B .a4-64=(a2 +8) (a +2 2 ) (a -2 2 )C .a4+1 =(a2 -1 ) (a2 -… 相似文献
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<正> 记Z[i]为高斯整数环,G_2=GL(2,Z[i]),G_2~±={X∈G_2|det X=±1},G_2~±=SL(2,Z[i]),G_2和G_2~±的投影群记为PG_2和PG_2~±.(注意G_2~±的投影群等于PG_2~±,这很容易证明.)任一X∈G_2在PG_2中的像记为εX,任一X∈G_2~±在PG_2~±中的像记为±X,任一群G的自同构群记为A(G),G的换位子群记为G’.在全文中记X为X中元素取复数共轭所得之阵,并记 相似文献
11.
Convexly independent sets 总被引:2,自引:0,他引:2
A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family of mutually disjoint compact convex sets such that any subfamily of at mostk members of is convexly independent, but no subfamily of sizen is. 相似文献
12.
设G是三维实李代数so(3)的复化李代数,A=C[T_1~(±1),t_2~(±2)]为复数域上的多项式环.设L(t_1,t_2,1)=G(?)_cA,d_1,d_2为L(t_1,t_2,1)的度导子.最近我们研究了李代数L(t_1,t_2,1)的自同构群结构.研究扭的Multi-loop代数L(t_1,t_2,1)(?)(Cd_1(?)Cd_2)的导子以及triple导子结构. 相似文献
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<正> 序言.在同倫論中,常常需要考慮滿足這種性質的拓撲空間X設Y為任意的一個正規空間,B為Y的任何一個非空閉集,任何一個由B×(0,1)+Y×(0)到X的映像都可以扩充為一個由Y×(0,1)到X的映像,我們稱這種性質為絕對同倫扩充性質,具有這種性質的空間以及用AHE表示.Borsuk曾經介紹這樣一個重要的定理: 相似文献
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u1,u2…是独立、同分布于(0,1)区间上均匀分布的随机变量.本文证明了1-u1u2…uk的n-1阶矩(n≥1)是以调和数的部分和ζn(r)=∑j=1n 1/jr,r≥1为变元的指数型完全Bell多项式,因此Riemann-Zeta函数ζ(k),k≥2能够被展开成第一类无符号Stirling数s(n,k)的级数,从而计算出与ζn(r)有关的全部6个五阶和式.它们都是ζ(5)与ζ(2)ζ(3)的有理组合. 相似文献
15.
Christopher J. Winfield 《Journal of Geometric Analysis》2001,11(2):343-362
In this article the following class of partial differential operators is examined for local solvability: Let P(X, Y) be a homogeneous polynomial of degree n ≥ 2 in the non-commuting variables X and Y. Suppose that the complex polynomial P(iz, 1) has distinct roots and that P(z, 0) = zn. The operators which we investigate are of the form P(X, Y) where X = δx and Y = δy + xδw for variables (x, y, w) ∈ ?3. We find that the operators P (X, Y) are locally solvable if and only if the kernels of the ordinary differential operators P(iδx, ± x)* contain no Schwartz-class functions other than the zero function. The proof of this theorem involves the construction of a parametrix along with invariance properties of Heisenberg group operators and the application of Sobolev-space inequalities by Hörmander as necessary conditions for local solvability. 相似文献
16.
László Babai 《Geometriae Dedicata》1977,6(3):331-337
Groups which are not isomorphic to the symmetry group of any vertextransitive polytope (of any dimension) are characterized
as generalized dicyclic, or abelian groups but not elementary 2-groups. The same class of groupsG is also characterized by the existence of a permutation groupP acting onG, containingG* (the regular representation ofG) as a proper subgroup, such that the members of the stabilizerP
u
of the unitu ε G take everyg ε G tog
±1. 相似文献
17.
Kevin P. Costello 《Israel Journal of Mathematics》2013,194(1):359-394
If f(x 1, …, x n ) is a polynomial dependent on a large number of independent Bernoulli random variables, what can be said about the maximum concentration of f on any single value? For linear polynomials, this reduces to one version of the classical Littlewood-Offord problem: Given nonzero constants a 1, …,a n , what is the maximum number of sums of the form ±a 1 ± a 2 ± … ± a n which take on any single value? Here we consider the case where f is either a bilinear form or a quadratic form. For the bilinear case, we show that the only forms having concentration significantly larger than n ?1 are those which are in a certain sense very close to being degenerate. For the quadratic case, we show that no form having many nonzero coefficients has concentration significantly larger than n ?1/2. In both cases the results are nearly tight. 相似文献
18.
Adaptive estimates for autoregressive processes 总被引:1,自引:0,他引:1
Rudolf Beran 《Annals of the Institute of Statistical Mathematics》1976,28(1):77-89
Let {X
t
:t=0, ±1, ±2, ...} be a stationaryrth order autoregressive process whose generating disturbances are independent identically distributed random variables with
marginal distribution functionF. Adaptive estimates for the parameters of {X
t
} are constructed from the observed portion of a sample path. The asymptotic efficiency of these estimates relative to the
least squares estimates is greater than or equal to one for all regularF. The nature of the adaptive estimates encourages stable behavior for moderate sample sizes. A similar approach can be taken
to estimation problems in the general linear model.
This research was partially supported by National Science Foundation Grant GP-31091X. American Mathematical Society 1970 subject
classification. Primary 62N10; Secondary 62G35. Key words and phrases: autoregressive process, adaptive estimates, robust
estimates. 相似文献
19.
Summary Certain t* elements of an abstract algebra are called independent if every equation satisfied by these elements is identically
true in the algebra [2]. For finite algebras we have: Given an integert*>3, everyt* elements are independent if every operation oft* variables is trivial, i. e. if it is identically equal to one of the variables (Th. 1). Ift*≤3, then there exists an algebra in which everyt* elements are independent but not every operation oft* variables is trivial; moreover ift*=3, then n is the number of elements of such an algebra if n=2 or 4 (mod 6 and n>3 (Th. 2). 相似文献
20.
<正> 设 K 是一个有限单形复合形,我们恒可视 K 为一充分高维数 N 的欧氏空间中的欧氏复合形,此时其所定空间将记为(?).在研究 K 是否可实现于某一确定维数 m 的欧氏盘间R~m 中的时候,我们曾引进下面的一些定义(见[1],记号略有不同): 相似文献