2-23-2005
... Let us show that there exists a vector that when added to v yields the 0 vector. Define –v = (-v1,-v2) Theorem: v + (-v) = 0 Proof: v+(-v)=(v1,v2)+(-v1,-v2)= (v1+(-v1),v2+(-v2))=(0,0) = 0 ...
... Let us show that there exists a vector that when added to v yields the 0 vector. Define –v = (-v1,-v2) Theorem: v + (-v) = 0 Proof: v+(-v)=(v1,v2)+(-v1,-v2)= (v1+(-v1),v2+(-v2))=(0,0) = 0 ...
1 Approximate Counting by Random Sampling
... (b) Using the random generator Rand[0,1], design a randomized algorithm to achieve the desired goal. Give the number of black box accesses to the function f and the number of accesses to Rand[0,1] used by your algorithm. 2. Estimating the (Unknown) Fraction of Red Balls. Suppose a bag contains an un ...
... (b) Using the random generator Rand[0,1], design a randomized algorithm to achieve the desired goal. Give the number of black box accesses to the function f and the number of accesses to Rand[0,1] used by your algorithm. 2. Estimating the (Unknown) Fraction of Red Balls. Suppose a bag contains an un ...
Discrete Math Notes 1 The Twelve-Fold Way
... pair. With this definition, the number of functions from X into Y is 1 if X is empty, and 0 if Y is empty but X is not. Discussed the notion of statements about elements of the empty set being vacuously true, motivated, for example, by the equivalence of an implication and the contrapositive stateme ...
... pair. With this definition, the number of functions from X into Y is 1 if X is empty, and 0 if Y is empty but X is not. Discussed the notion of statements about elements of the empty set being vacuously true, motivated, for example, by the equivalence of an implication and the contrapositive stateme ...
Bertrand`s Theorem - New Zealand Maths Olympiad Committee online
... The two binomial coefficients on the left are equal and we get (a). (b) If n is even, then it is pretty easy to prove that the middle binomial coefficient is the largest one. In (5) we have n + 1 summand but we group the two ones together and we get n summands among which the middle binomial coeffic ...
... The two binomial coefficients on the left are equal and we get (a). (b) If n is even, then it is pretty easy to prove that the middle binomial coefficient is the largest one. In (5) we have n + 1 summand but we group the two ones together and we get n summands among which the middle binomial coeffic ...
notes - Department of Computer Science and Engineering, CUHK
... This is an example of a homogeneous linear recurrence. Such recurrences can be solved using the following guess verify method. Initially, we forget about the “base cases” f (0) = 1, f (1) = 1 and focus on the equations (4). We look for solutions of the type f (n) = xn for some nonzero real number x. ...
... This is an example of a homogeneous linear recurrence. Such recurrences can be solved using the following guess verify method. Initially, we forget about the “base cases” f (0) = 1, f (1) = 1 and focus on the equations (4). We look for solutions of the type f (n) = xn for some nonzero real number x. ...
1 Introduction to Random Variables
... Example. Sometimes we base a model for a random variable on data collected from a sample. For example, an industrial psychologist administered a personality inventory test for passive-aggressive traits to 150 employees. Individuals were rated on a scale from 1 to 5 (passive to aggressive). The resul ...
... Example. Sometimes we base a model for a random variable on data collected from a sample. For example, an industrial psychologist administered a personality inventory test for passive-aggressive traits to 150 employees. Individuals were rated on a scale from 1 to 5 (passive to aggressive). The resul ...
Asymptotic theory
... Approximate or asymptotic results are an important foundation of statistical inference. Some of the main ideas are discussed below. The ideas center around the fundamental theorem of statistics, laws of large numbers (LLN ), and central limit theorems (CLT ). The discussion includes definitions of c ...
... Approximate or asymptotic results are an important foundation of statistical inference. Some of the main ideas are discussed below. The ideas center around the fundamental theorem of statistics, laws of large numbers (LLN ), and central limit theorems (CLT ). The discussion includes definitions of c ...
formula
... Recall that is a special constant (not a variable). It is, in fact, defined to be the number that makes this formula work. It is known that in decimal form, has an infinite number of digits with no repeating pattern. Your calculator knows the first ten digits or so. ...
... Recall that is a special constant (not a variable). It is, in fact, defined to be the number that makes this formula work. It is known that in decimal form, has an infinite number of digits with no repeating pattern. Your calculator knows the first ten digits or so. ...
PROBABILISTIC TRACE AND POISSON SUMMATION FORMULAE
... 1. Introduction The classical Poisson summation formula is a well-known result from elementary Fourier analysis. It states that for a suitably well–behaved function f : R → C (and typically f is in the Schwartz space of rapidly decreasing functions), we have X X ...
... 1. Introduction The classical Poisson summation formula is a well-known result from elementary Fourier analysis. It states that for a suitably well–behaved function f : R → C (and typically f is in the Schwartz space of rapidly decreasing functions), we have X X ...
