End of year Exam Preparation questions File
... The mean of the ten numbers listed below is 5.5. 4, 3, a, 8, 7, 3, 9, 5, 8, 3 (a) ...
... The mean of the ten numbers listed below is 5.5. 4, 3, a, 8, 7, 3, 9, 5, 8, 3 (a) ...
Full text
... To obtain a partial generalization of Theorem II of Horadam and the corresponding proposition of 5ubbaRao,we first define {U^} * a fundamental sequence of order r; we illustrate its fundamental nature by showing that any linear recursive sequence of order v can be expressed in terms of {U^}. We defi ...
... To obtain a partial generalization of Theorem II of Horadam and the corresponding proposition of 5ubbaRao,we first define {U^} * a fundamental sequence of order r; we illustrate its fundamental nature by showing that any linear recursive sequence of order v can be expressed in terms of {U^}. We defi ...
Simple Block Code Parity Checks
... Rules for Modular arithmetic Fact: If a ≡m a′ and b ≡m b′, then a + b ≡m a′ + b′ and a ∙ b ≡m a′ ∙ b′. Proof: a ≡m a′ and b ≡m b′ means that a = a′ + im and b = b′ + jm, so a + b = a′ + b′ + (i + j)m and a ∙ b = a′ ∙ b′ + a′jm + b′im + ijm2. QED Multiplicative inverses may not exist for some number ...
... Rules for Modular arithmetic Fact: If a ≡m a′ and b ≡m b′, then a + b ≡m a′ + b′ and a ∙ b ≡m a′ ∙ b′. Proof: a ≡m a′ and b ≡m b′ means that a = a′ + im and b = b′ + jm, so a + b = a′ + b′ + (i + j)m and a ∙ b = a′ ∙ b′ + a′jm + b′im + ijm2. QED Multiplicative inverses may not exist for some number ...
A simple D -sampling based PTAS for k-means and other Clustering problems
... the set of points of P which are closer to a particular center than other centers. It is also easy to show that the center of any cluster must be the mean of the points in it. In most applications, the parameter k is a small constant. However, this problem turns out to be NP-hard even for k = 2 [13 ...
... the set of points of P which are closer to a particular center than other centers. It is also easy to show that the center of any cluster must be the mean of the points in it. In most applications, the parameter k is a small constant. However, this problem turns out to be NP-hard even for k = 2 [13 ...
![arXiv:1003.5939v1 [math.CO] 30 Mar 2010](http://s1.studyres.com/store/data/016290525_1-37241e0159a202e5bf035fd4e5a48270-300x300.png)
lect02_matlab_fundamentals
... – Variables are arrays of numbers. – You name the variables (as the programmer) and assign them numerical values. – You execute the assignment command to place the variable in the workspace memory (memory is part of hardware used for storing ...
... – Variables are arrays of numbers. – You name the variables (as the programmer) and assign them numerical values. – You execute the assignment command to place the variable in the workspace memory (memory is part of hardware used for storing ...
Document
... Example: {1, 3, 4, 6, 8} Example: {1, 2, 3, …, 66} or {2, 4, 6, 8, …} Example: {x : x is an even positive integer} which we read as: the set of x such that x is an even positive integer Example: {x : x is a prime number less than a million} which we read as: The set of x such that x is a prime numbe ...
... Example: {1, 3, 4, 6, 8} Example: {1, 2, 3, …, 66} or {2, 4, 6, 8, …} Example: {x : x is an even positive integer} which we read as: the set of x such that x is an even positive integer Example: {x : x is a prime number less than a million} which we read as: The set of x such that x is a prime numbe ...
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)