Section 5. Geometric Series
... we can keep this up, we are forced to conclude that the total length of the rational numbers can be made smaller than any positive number, no matter how tiny. In other words, the total length of the rational numbers must be zero. 5.4. Application 3: The Cantor Set. What is the length of the Cantor S ...
... we can keep this up, we are forced to conclude that the total length of the rational numbers can be made smaller than any positive number, no matter how tiny. In other words, the total length of the rational numbers must be zero. 5.4. Application 3: The Cantor Set. What is the length of the Cantor S ...
lectures 1-4
... • Theoretical (e.g. spectral test), but mostly address whole period, not guaranteed to be meaningful for shorter streams. • Empirical tests, claim to look for various aspects of (non)randomness of a given stream. Consist of computing a certain number using the given stream, comparing with result of ...
... • Theoretical (e.g. spectral test), but mostly address whole period, not guaranteed to be meaningful for shorter streams. • Empirical tests, claim to look for various aspects of (non)randomness of a given stream. Consist of computing a certain number using the given stream, comparing with result of ...
6.4 Recursion Formulas
... without knowing the previous term. For example, the tenth term in the sequence determined by the formula tn = 2n + 3 is 2(10) + 3, or 23. It is sometimes more convenient to calculate a term in a sequence from one or more previous terms in the sequence. Formulas that can be used to do this are called ...
... without knowing the previous term. For example, the tenth term in the sequence determined by the formula tn = 2n + 3 is 2(10) + 3, or 23. It is sometimes more convenient to calculate a term in a sequence from one or more previous terms in the sequence. Formulas that can be used to do this are called ...
Information geometry on hierarchy of probability distributions
... the function space were given by Pistone and his coworkers [35], [36] and are now developing further. The present paper shows how information geometry gives an answer to the problem of invariant decomposition for hierarchical systems of probability distributions. This leads to a new invariant decomp ...
... the function space were given by Pistone and his coworkers [35], [36] and are now developing further. The present paper shows how information geometry gives an answer to the problem of invariant decomposition for hierarchical systems of probability distributions. This leads to a new invariant decomp ...
Lecture Notes for Section 8.1
... If a nonempty set S of real numbers has a lower bound, then it has a greatest lower bound. Equivalently, if S has an upper bound, then it has a least upper bound. Note that this is an axiom; it a statement we accept as being true without proof. Axioms form the foundation upon which all other theorem ...
... If a nonempty set S of real numbers has a lower bound, then it has a greatest lower bound. Equivalently, if S has an upper bound, then it has a least upper bound. Note that this is an axiom; it a statement we accept as being true without proof. Axioms form the foundation upon which all other theorem ...
MA3H2 Markov Processes and Percolation theory
... random walk events were are after counting corresponding set of paths. The following result is an important tool for this counting. Notation: Nn (a, b) = ] of possible paths from (0, a) to (n, b). We denote by Nn0 (a, b) the number of possible paths from (0, a) to (n, b) which touch the origin, i.e. ...
... random walk events were are after counting corresponding set of paths. The following result is an important tool for this counting. Notation: Nn (a, b) = ] of possible paths from (0, a) to (n, b). We denote by Nn0 (a, b) the number of possible paths from (0, a) to (n, b) which touch the origin, i.e. ...
CZ2105 Lecture 2
... computes how many times each value occured. >> for k = 1:100 >> y = rand; >> x(k) = round(6*y+1/2); >> end >> for val = 1:6 >> numbers(val) = sum(x == val); >> end >> numbers numbers = 17 18 19 18 17 ...
... computes how many times each value occured. >> for k = 1:100 >> y = rand; >> x(k) = round(6*y+1/2); >> end >> for val = 1:6 >> numbers(val) = sum(x == val); >> end >> numbers numbers = 17 18 19 18 17 ...
Q. 1 – Q. 5 carry one mark each.
... It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________. (A ...
... It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________. (A ...
