Name: Date: Period: UNIT 5 TEST REVIEW: SEQUENCES AND
... circles. She notices that the wooden circles are put in diagonal lines starting in a corner. The first diagonal “row” has 1 wooden circle. The second diagonal row has 2 wooden circles, the third row has 3, and so on. How many wooden circles does it take to make up half of her placemat if one half ha ...
... circles. She notices that the wooden circles are put in diagonal lines starting in a corner. The first diagonal “row” has 1 wooden circle. The second diagonal row has 2 wooden circles, the third row has 3, and so on. How many wooden circles does it take to make up half of her placemat if one half ha ...
Random Numbers, Math Library
... Now, consider a more complicated example that includes multiple function calls within a single line of code: double a = 1, b = 4, c = -21; double x1 = (-b + sqrt(pow(b,2) - 4*a*c))/(2*a); Let’s go through the basic order in which everything gets evaluated in this statement: 1) The pow function call ...
... Now, consider a more complicated example that includes multiple function calls within a single line of code: double a = 1, b = 4, c = -21; double x1 = (-b + sqrt(pow(b,2) - 4*a*c))/(2*a); Let’s go through the basic order in which everything gets evaluated in this statement: 1) The pow function call ...
continued fractions - University of Hawaii Mathematics
... Theorem 14]) for a complete proof. We, however, provide some remarks concerning this result below. In particular, we will explain at some point, what the convergence means. Theorem 1. An infinite continued fraction converges and defines a real number. There is a one-to-one correspondence between • a ...
... Theorem 14]) for a complete proof. We, however, provide some remarks concerning this result below. In particular, we will explain at some point, what the convergence means. Theorem 1. An infinite continued fraction converges and defines a real number. There is a one-to-one correspondence between • a ...
Chapter 3 Gambling, random walks and the Central Limit Theorem
... We are now ready to present our gambler with a mathematically sound advice: yes, it is possible to exploit large mean values present in this game and win a lot. You just need to play this game at least six hundred trillion times. Oh and if you plan to start playing each game with a pound, do not for ...
... We are now ready to present our gambler with a mathematically sound advice: yes, it is possible to exploit large mean values present in this game and win a lot. You just need to play this game at least six hundred trillion times. Oh and if you plan to start playing each game with a pound, do not for ...
DIOPHANTINE APPROXIMATION OF COMPLEX NUMBERS
... linear forms with complex conjugated coefficients zik and another r = n − 2s linear forms Y2s+1 , . . . Yn with real coefficients. Then there exist integers x1 , . . . , xn , not all zero, such that ...
... linear forms with complex conjugated coefficients zik and another r = n − 2s linear forms Y2s+1 , . . . Yn with real coefficients. Then there exist integers x1 , . . . , xn , not all zero, such that ...
The strong law of large numbers - University of California, Berkeley
... A well known unsolved problem in the theory of probability is to find a set of necessary and sufficient conditions (nasc's) for the validity of the strong law of large numbers (SLLN) for a sequence of independent random variables. This problem will not be solved in the present paper. To avoid a poss ...
... A well known unsolved problem in the theory of probability is to find a set of necessary and sufficient conditions (nasc's) for the validity of the strong law of large numbers (SLLN) for a sequence of independent random variables. This problem will not be solved in the present paper. To avoid a poss ...
Performance of Initial Synchronization Schemes for WCDMA
... Now, two equivalent expressions for FTd |H1 (γ) can be derived [10]. The first one is restricted to the case, that all eigenvalues are distinct and is based on a partial fractional expansion and inverse Fourier transform of the characteristic function yielding the pdf of Td . The cdf is then obtaine ...
... Now, two equivalent expressions for FTd |H1 (γ) can be derived [10]. The first one is restricted to the case, that all eigenvalues are distinct and is based on a partial fractional expansion and inverse Fourier transform of the characteristic function yielding the pdf of Td . The cdf is then obtaine ...
PowerPoint presentation for "Continued Fractions"
... Find cfe of 29.46. Read off first few rational approximations 29/1, 59/2, 206/7,..then simulate Saturn’s motion relative to Earth by making one gear with 7 teeth and one with 206 ...
... Find cfe of 29.46. Read off first few rational approximations 29/1, 59/2, 206/7,..then simulate Saturn’s motion relative to Earth by making one gear with 7 teeth and one with 206 ...
Testing Booleanity and the Uncertainty Principle
... denote the Fourier transform by fˆ, and think of it too as a function from {−1, 1}n to R. We say that f is Boolean if f (x) = 1 or f (x) = −1 for all x in its domain. An interesting question in the field of discrete Fourier analysis of Boolean functions is the following: what does the fact that f is ...
... denote the Fourier transform by fˆ, and think of it too as a function from {−1, 1}n to R. We say that f is Boolean if f (x) = 1 or f (x) = −1 for all x in its domain. An interesting question in the field of discrete Fourier analysis of Boolean functions is the following: what does the fact that f is ...
Full text
... histories of length n starting at level k and ending at level /, while the reciprocal Tchebycheff polynomials of degree h are used to derive generating functions for histories of height < h. In this context, the Tchebycheff polynomials are distinguished among the family of Fibonacci-like polynomials ...
... histories of length n starting at level k and ending at level /, while the reciprocal Tchebycheff polynomials of degree h are used to derive generating functions for histories of height < h. In this context, the Tchebycheff polynomials are distinguished among the family of Fibonacci-like polynomials ...
ON BERNOULLI DECOMPOSITIONS FOR RANDOM VARIABLES
... with a constant CX < ∞ which depends on the uniform bounds on the distributions of {Xj }. The proof employs the Bernoulli representation along with the combinatorial bounds of Sperner [S], and the more general LYM lemma [E]. The use of combinatorial estimates for concentration bounds first appeared ...
... with a constant CX < ∞ which depends on the uniform bounds on the distributions of {Xj }. The proof employs the Bernoulli representation along with the combinatorial bounds of Sperner [S], and the more general LYM lemma [E]. The use of combinatorial estimates for concentration bounds first appeared ...
Empirical Bernstein Bounds and Sample Variance Penalization
... over L , analogous to Corollary 2, and provides us with a view of the loss class which is blurred for hypotheses of large sample variance, and more in focus for hypotheses of small sample variance. We note that an analogous result to Theorem 4 is given by Audibert et al. [2]. Our technique of proof ...
... over L , analogous to Corollary 2, and provides us with a view of the loss class which is blurred for hypotheses of large sample variance, and more in focus for hypotheses of small sample variance. We note that an analogous result to Theorem 4 is given by Audibert et al. [2]. Our technique of proof ...
B. The Binomial Theorem
... just the binomial coefficient for power n. In this case the number of terms in the expansion is finite, and equal to n + 1. The coefficient C(n, k) is 0 eq:casepn if k > n, because one of the factors in the numerator of (B-17) is 0. For example, C(n, n + 1) = 0 because the final factor is n − (n + 1 ...
... just the binomial coefficient for power n. In this case the number of terms in the expansion is finite, and equal to n + 1. The coefficient C(n, k) is 0 eq:casepn if k > n, because one of the factors in the numerator of (B-17) is 0. For example, C(n, n + 1) = 0 because the final factor is n − (n + 1 ...