continuous distributionsand the poisson process

... permute the coins randomly, and then flip each of the coins The first and second coins come up heads, and the third comes up tails What is the probability that the first coin is the biased one? The ... the outcomes of the coin fl ips, each of the three coins is equally likely to be the biased one Let Ei be the event that the i th coin flipped is the biased one, and let B be the event that the ... repeatedly the following: choose one ball from the bin uniformly at random , and then put the bal l back i n the bin with another bal l of the same color We repeat u ntil there are n bal l s in the...

Ngày tải lên: 14/07/2016, 15:42

... have not proved Girsanov’s Theorem We will not prove it completely, but here is the beginning of the proof Lemma 1.55 Using the notation of Girsanov’s Theorem, we have the martingale property fe ... Under I , the process B t;  t  T , is a Brownian motion P Caveat: This theorem requires a technical condition on the size of If IE exp  ZT 2 u du  1; everything is OK We make the following ... e T Under IP , B T  is normal with Means change, variances don’t When we use the Girsanov Theorem to change the probability measure, means change but variances not Martingales may be destroyed...

Ngày tải lên: 18/10/2013, 03:20

... n i=0 fi i Let α be a zero of the function Q(z) Then α is a zero of some polynomial fi (0 n + 1) By the hypothesis that the polynomials are relatively prime, there exists a number v(0 v n + ... deg g(x) Here the notation deg f (x) means the degree of polynomial f (x) From the properties of polynomial, we have Proposition 2.1 If ϕ1 and ϕ2 are the rational functions on F, then 1) deg(ϕ1 ... Generalied Mason’s Theorem 35 Proof of the main theorem Let ϕ(x) = f (x) ≡ be a rational function, where f (x), g(x) are non - zero and g(x) relatively prime polynomials on F The degree of ϕ(x),...

Ngày tải lên: 13/02/2014, 04:20

... that N1 N2 N Then (4.4) log p = N1

Ngày tải lên: 06/03/2014, 08:21

... of D there is a conformal map f of the disk which extends continuously to E and equals g there An earlier verison of the proof of Theorem used a characterization of these sets as exactly the compact ... Wk be the interior of the closure of the part of W = Φ(D) separated from by the arc of the circle T between the angles corresponding to xk and xk+1 Then Wk can be conformally mapped to the by ... metric) to the path in X between these points This observation will be used in the proof of the next lemma This completes the proof of the induction step and hence completes the proof of Theorem...

Ngày tải lên: 22/03/2014, 20:21

... of the cube one after the other, the permutation of the tetrahedra so obtained is the product of the permutations of the tetrahedra corresponding to these rotations Therefore the mapping of the ... of these cubes are the diagonals of the 12 faces of the dodecahedron Kepler had invented these cubes in his Harmonia Mundi to describe the distances of the planets from the Sun I had used them ... monodromy of the algebraic function defined by the quintic equation is the non-soluble group of the 120 permutations of the roots This theory provides more than the Abel Theorem It shows that the insolvability...

Ngày tải lên: 31/03/2014, 14:57

... Even there, we saw at the end that there are serious problems with the model It may be that there are even more serious problems with the Cellular Automaton model for the way the universe works The ... each other's orientation, although not by any known mechanism More recent tests set the orientation of the the polarizers randomly after the electrons have left the source The results of these ... these projections exist only as abstractions, the three-dimensional reality is neither of these What is actually found [in the experimental tests of Bell's theorem] is that the behavior of the...

Ngày tải lên: 05/06/2014, 10:58

... for any ε >0 By the argminimality of Tμx (see Lemma 2.2), Tμx = Px □ In order to obtain the Rodé’s theorem (Theorem 1.1) in the framework of CAT(0) spaces, we need to restrict the asymptotically ... Fixed Point Theory and Applications 2011, 2011:34 http://www.fixedpointtheoryandapplications.com/content/2011/1/34 Page of 14 Further, for each x Î C, the limit point of {Tμα x}is the same for ... [[9], p 163]), the following are equivalent for a geodesic space X: (i) X is a CAT(0) space (ii) X satisfies the (CN) inequality: If x0, x1 Î X and x0 ⊕x1 is the midpoint of x0 and x1, then d2 (y,...

Ngày tải lên: 21/06/2014, 01:20

... that the point z, obtained in the Theorem 5, satisfies the statement of the theorem Following the same notation in the proof of Theorem 5, it is needed to show that x ∉ S(z) for x ≠ z Assume the ... claim □ The following theorem is an extension of the result of Caristi ([9]; Theorem 2.1) Theorem Let (X, p) be a complete PMS,  : X ® ℝ+ a lower semi -continuous (l s.c) function on X Then, each ... map on (X, p) The following lemma will be used in the proof of the main theorem Lemma (see, e.g [8,7]) Let (X, p) be a complete PMS Then (A) If p(x, y) = then x = y, (B) If x ≠ y, then p(x, y)...

Ngày tải lên: 21/06/2014, 02:20

... convergence is called the Shannon-McMillan theorem or the entropy theorem or the asymptotic equipartition property AEP in information theory The Shannon-McMillan theorem on the Markov chain has ... extensively see 2, In the recent years, with the development of the information theory scholars get to study the Shannon-McMillan theorems for the random field on the tree graph see The tree models ... measures of the deviation between the arbitrary random fields and the Markov chain fields on the generalized Bethe tree Main Results Theorem 2.1 Let X {Xt , t ∈ T} be an arbitrary random field on the generalized...

Ngày tải lên: 21/06/2014, 05:20

... then there exits y ∈ X such that ϕ y

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... 2n−3 + 3, and the extremal graph is (up to isomorphism) K3,n−3 , the second extremal graph being K3,n−3 − e There is a class of algorithms which yield all irreducible coverings for the set-covering ... covering by n − k cliques Theorem 2.1 Let k ≥ If the graph G of order n has an irreducible covering by n − k k cliques, then ω(G) ≤ k + if k = or and ω(G) ≤ k/2 if k ≥ Moreover, these bounds are sharp ... xj ∈ / E(G) since otherwise A ∪ {xi , xj } induces a complete subgraph in G, thus contradicting the hypothesis that ci is a clique This implies that each clique c in G has the form {t1 , ,...

Ngày tải lên: 07/08/2014, 06:23

... The diagonal entries are Except N11 , all the other entries in the first row are We construct the remaining entries of N (G) by induction on the rank The base case is rank It corresponds to the ... ); i < v(G), j < I, the remaining parts of the theorem follow There is another way of proving the N -matrix reconstructibility of the characteristic ¯ polynomial Let G denote the complement of ... G there is only one unknown on the RHS of Equation (29) All G(v(G), l, (ni, mi )l ) i=1 other terms on the RHS are known by the induction hypothesis We can compute the unknown term to obtain the...

Ngày tải lên: 07/08/2014, 13:21

... sufficient The upper bound of the preceding theorem is better than O’Rourke’s bound of (n+2h)/4 when the number of holes h is large This is because n, the total number of vertices, includes the vertices ... vertices on the boundary of the polygon formed by cycle C If a quadrilateral has two vertices on the exterior boundary and two on the boundary of the hole, it is called balanced, otherwise it ... label the vertices on the Q external cycle with v1 , v2 , , v2k , for some k ≥ 2, and the vertices on the internal cycle with v2k+1 , , vm , in the clockwise manner (See Fig 6.) Then it...

Ngày tải lên: 07/08/2014, 13:21

... Landau’s theorem is the special case where T has no edges the electronic journal of combinatorics 16 (2009), #N2 As a referee observed, because of the presence of the quantity γ(K), whether or not the ... n The transversal S is an independent transversal of A provided that S is an independent set of the matroid M Theorem 2.2 (Rado’s theorem) The family A = (A1 , A2 , , An ) of subsets of the ... of Landau’s theorem using Rado’s theorem The necessity of (1) is obvious Now assume that (1) holds Let X = {(i, j); ≤ i, j ≤ n, i = j} Consider the matroid M on X whose circuits are the n disjoint...

Ngày tải lên: 07/08/2014, 21:21

... 2.4: The “if” part in Theorem(2.3), which is a particular case of the AlexandrovFenchel inequalities, is not simple, but was proved seventy years ago [1] The proof of the “only if” part in Theorem(2.3) ... = 0≤j≤c tj Then the polynomial R1 (t)R2 (t) := R3 (t) = 0≤k≤l+d ck tk , where the sequence c = (c0 , , cl+d ) is the convolution, c = a b It follows from the “only if”!p part of Theorem(2.3) ... ab) and the number c2 a2 =2 c4 c6 b (1 − ab) converges to zero if the positive numbers a, b, a converge to zero b The reader can find further implications (and their generalizations) of Theorem(2.3)...

Ngày tải lên: 07/08/2014, 21:21