create your independent and dependent variables

... similarity was found between the sense and antisense strands of PRE-ISS, suggesting a sequence -independent silencer mechanism Third, both the sense and antisense strands of PRE-ISS form complex secondary ... pre-mRNA transport and splicing No significant sequence similarity was found between the sense and antisense strands of PRE-HBV1253–1582 (Fig S2A), indicating that a sequence -independent silencer ... two stems (S1 and S2) and a hexanucleotide loop (L1), whereas HP2 contains a 9-bp stem (S3) and a 25-nucleotide large loop (L2) HP1 and HP2 are joined by an 11-nucleotide single-stranded region...

Ngày tải lên: 28/03/2014, 23:20

... distributions can arise as limits of distributions of sums of independent random variables Consider, for each n, a collection of independent random variables, Xnl , Xn2, , Xnkn The Xnk are said to be ... { [a, b) } = F (b) - F (a), and X (w) = w 21 CONVERGENCE OF DISTRIBUTIONS Let X and Y be independent random variables with respective distribution functions F1 and F2 The distribution function ... Sums of Independent Random Variables" by B V Gnedenko and A N Kolmogorov, whose publication in 1949 inspired much of the research we describe Chapters 2-5 treat problems about sums of independent, ...

Ngày tải lên: 08/04/2014, 12:28

... policy in your handbook • standard language that you can cut and paste into your handbook (or, if there is no standard way to word a policy, an example of what such policies look like and detailed ... happens, it’s time to consider revising the entire handbook and handing out a new edition to your employees Distributing Your Handbook Once your employee handbook is complete, it’s time to distribute ... existing handbook) using this book, you need to understand your company’s legal obligations as an employer in your state If you need information on employment law or your company’s H/ H/4 CREATE YOUR...

Ngày tải lên: 18/04/2014, 14:04

... distributions can arise as limits of distributions of sums of independent random variables Consider, for each n, a collection of independent random variables, Xnl , Xn2, , Xnkn The Xnk are said to be ... { [a, b) } = F (b) - F (a), and X (w) = w 21 CONVERGENCE OF DISTRIBUTIONS Let X and Y be independent random variables with respective distribution functions F1 and F2 The distribution function ... Zn= Xl+X2+ + Xn _ An Bn (2.1 3) of stationarily dependent random variables In this section we establish this result for independent random variables ; the general case is dealt with in Theorem...

Ngày tải lên: 27/06/2014, 03:20

... distributions can arise as limits of distributions of sums of independent random variables Consider, for each n, a collection of independent random variables, Xnl , Xn2, , Xnkn The Xnk are said to be ... { [a, b) } = F (b) - F (a), and X (w) = w 21 CONVERGENCE OF DISTRIBUTIONS Let X and Y be independent random variables with respective distribution functions F1 and F2 The distribution function ... of X, and is denoted by the symbol E(X) I f X is a random vector with values in R" and distribution F, and is a Borel measurable function from R" to R, then (X) is a random variable, and E O...

Ngày tải lên: 02/07/2014, 20:20

... We first show that A(y) < AN (,/,ZN+1 + ) e , where A N and s are independent of and y, and E < To this we remark that ( 2.4.17) E is independent also of N, lc(y)I = exp { -Re y -2 b(y)} = sine ... 1-n -1 n- a , ,c ), and use Theorem 5.1 § Domains of attraction Let X1 , X2 , be a sequence of independent random variables, with the same distribution function F (x), and set Zn= Xl+X2+ ... in § We shall prove the following result I f* a sequence X1 , X2 , of independent, identically distributed random variables is such that the distribution of the normed sum )/B -A +X Zn =...

Ngày tải lên: 02/07/2014, 20:20

... -6) (4.4.5) m Proof Let ~ , b2, be independent and identically distributed random variables taking only the values and 1, with respective probabilities b and a Bernstein's inequality (cf § 7.5) ... necessary and sufficient that the interval h be maximal and that x dF(x) = O(z - b) ~xI~z Theorem If the independent variables Xj have the same lattice distribution with step h, and have E(Xj) = and ... lattice distributions Let the independent random variables X1 , X2 , , Xn , (4.2 1) have the same distribution, concentrated on the arithmetic progression {a+kh}, and write Zn =X1 +X2+ +Xn...

Ngày tải lên: 02/07/2014, 20:20

... ), write i = 27r/h and define S (x) and d,,(t) as in § 3.3 Theorem 5.3 If X1 , X2 , are independent random variables with the same distribution F belonging to L h and having finite third ... in Lp, and the remaining sections deal with the case of normal convergence § Domains of attraction of stable laws in the L metric P Let X1 , X2 , be a sequence of independent random variables ... finite third moment, and write E(XX)=0, E(Xj2)=62, E(X,3)=a3, EIX;I3=J33 As before, the distribution function and characteristic function of X;, and the distribution function and characteristic...

Ngày tải lên: 02/07/2014, 20:20

... problem of characterising the possible limit laws for centralised and normalised sums of independent variables, i e the stable laws And of course there is a corresponding problem of local limit ... the asymptotic formula (6.1 6) can be very useful, and is often much easier to compute than the exact expression (6 5) Suppose that the random variables X; introduced at the beginning of the section ... to order (s+3) Thus if we have two sequences A } and {Xj'}, both satisfying Cramer's condition, whose moments agree up to order (s + 3), and Z„ and Z ;, are the corresponding normalised sums,...

Ngày tải lên: 02/07/2014, 20:20

... computation, and if the constants in them are best possible, or nearly so Important among these is Bernstein's inequality ([7], pages 161-165) We assume that the independent random variables X1 ... IM(z)l < exp(-sc E1) (7.2.14) on L2 and L4 Moreover, lexp (- cn2 z) = exp (- cn2 Re z) < , (7.2.15) I and therefore = O(exp(-nr7 (E ))) + (7.2.16) JL on L2 and L4 Moreover, lexp (- un- z) I ... integrand in (7.2.4) has the form M (z)" exp (- cn zx) (7.2.5) We shall suppose that c is chosen so small that c < a and that (M(z)I > in IzI < c (this being possible since M is continuous and...

Ngày tải lên: 02/07/2014, 20:20

... introduction of auxiliary random variables Since E (exp a JXX j) < oo , we may write, for Jhj

Ngày tải lên: 02/07/2014, 20:20

... P (n) } will certainly occur if the independent events {X > 6n " p(n)+01 and { 1(X2 + X3 + + X©)/ oni- } both occur Hence, by the central limit theorem and (9.2.2), < THE FUNDAMENTAL CONDITIONS ... /3 < and (9 2.5) contradicts (9.2.4) The case of (9.2 3) is treated similarly Theorem 2 For random variables of class (d) the condition (9.2 1) is necessary in order that [0, n" p (n)] and [- ... (9.2.8) for x > 0, and a similar condition for x < Hence 2x exp (xfl) g (x) dx = B exp (- xQ) x in x > Taking x =1, 2, 4, and adding, we get 00 exp (xQ) g (x) dx < oo , fi and combining this...

Ngày tải lên: 02/07/2014, 20:20

... of the independent events IX2 + +XJ/Gn2

Ngày tải lên: 02/07/2014, 20:20

... The event described in (11 4.1) occurs if both the independent events Xl >cniA(n)p(n)+8 ; JX2 +X3 + +X©J/cn < occur, and thus by (11 4.2) and the central limit theorem, P(zn > 2A(n) P (n)) ... Let XX be random variables with E (Xi) = 0, V (X;) = 1, and suppose that (11.2.2) is satisfied, where h (x) is a function of Class I We begin by following „ ; determine ° from (11 6) and set ... (n), 0] are zones of local normal attraction for variables in (d), and of integral normal attraction in general, and that [0, (log n)l p (n) ] and [ - (log n)4 p (n), 0] will not be so unless...

Ngày tải lên: 02/07/2014, 20:20

... auxiliary variables We now write XI = Xi +,J i , (i < n), where the d ; are independent, small normal variables, z1 EN(0, n -10), (12.3 1) and S©=Xi+Xz+ +Xn Then V (S©) = V (S©) + n -19 and the ... define el (~) = el , = , (ICI,< n 2a /P3 (n)) ( kkI > n 2, /P3 (n)) (12.3.4) Let X1 be independent random variables with probability density d17(x) = R -l e (hx)p(x) , dx (12.3.5) where R = For ... further independent random variable Yn EN(0, n") , (12.11 2) with characteristic function ~Y "' n (t)=exp (-2n t2) ( 12.11 3) The sum (X l + X2 + + Xn + Yn) has distribution function Fn (x) and...

Ngày tải lên: 02/07/2014, 20:20

... 2.2) Zn = Sn/6n- , and a modified random variable Z n = Zn + Yn /6n ( 13 3) , where Yn is a random variable, independent of the Xj , and having a normal distribution with mean and variance n " ... independent and identically distributed, with E(Xj)=0, V(Xj)=6 , and suppose that (13 1) is satisfied We prove that, for any monotonic function p ( n) -3 oo there exist positive constants c and ... ( 13.2.4) The distribution functions of Z n and n will be denoted by Fn (x) and Fn (x) respectively, and their characteristic functions by fn (t) and fn(t), so that n2"-1 t fn (t) = fn (t) eXp...

Ngày tải lên: 02/07/2014, 20:20

... (14.2.8) and (14.2 11) We now examine the second term in (14 2.12) The event X2 + + Xn ant > L (14.2.16) is independent of H , and implies that for some i, Xl > yn a /log n Arguing as before, and ... integral (14.3 8) the integrand is rational, non-zero on the real axis, has poles „ i and is of order O (~-"`) at infinity Moving the contour of integration upwards for t>,0 and downwards for t,

Ngày tải lên: 02/07/2014, 20:20

... , , ~n be independent DISTRIBUTIONS OF SUMS OF INDEPENDENT COMPONENTS 276 Chap 15 variables taking only the two values (with probability p) and (with probability q =1- p), and write C=~1+~_2+ ... function of a random variable X is the function QX (l) = Q(l) =sup P(x

Ngày tải lên: 02/07/2014, 20:20

... sequence of independent, identically distributed random variables , X-1, XO, X1, X2, forms a stationary process in the strict sense Let , ~ _ 1, ~0 ' b 1 ~2, be a sequence of independent, ... probability Since each random variable ~, measurable with respect to M, is the limit as n ' co with probability 1, of the random variables _ j ~n k=-cc k nx k -C n +1 n there exists one and only one transformation ... FO) Then F0 ) is absolutely continuous if and only if Xj can be represented by the sum Xj = Ck~k+j (16.7.1) k=-oo where Z Ick1 < 00 , and the random variables ~ j are orthogonal, with E gj =1...

Ngày tải lên: 02/07/2014, 20:20

... distribution of a random vector with characteristic function (17 3.1) The following properties are immediate consequences of the definition (1) The variables X1 , X2 , , Xn are independent if and only ... is of course clear that a strongly mixing process is necessarily regular A sequence of independent random variables is strongly mixing ; other examples will appear in ©© 17 3, 19.1, 19.2, 19 Theorem ... 2.2) follows If the variables ~, i are complex, then separating the real and imaginary parts, we again arrive at (17.2 2), with replaced by 16 Theorem 17 2.2 Let the random variables ~, q be measurable...

Ngày tải lên: 02/07/2014, 20:20