Sequences and summations
Sequences Definition: A sequence is a function from a subset of the set of integers (typically the set {0,1,2,...} or the set {1,2,3,...} to a set S. We use the notation an to denote the image of the integer n. ... • Infinite geometric series can be computed in the closed form
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CS 1652: Data Communication and Computer Networks …
people.cs.pitt.edufrom the application layer to the data-link layer. Concurrent with the lectures, you (in groups of two) will be building a functional TCP/IP stack and a small web server that will run on it.
Informal proofs - University of Pittsburgh
people.cs.pitt.eduInformal proofs Proving theorems in practice: • The steps of the proofs are not expressed in any formal language as e.g. propositional logic
MIPS Floating Point Instructions
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Foundations of Artificial Intelligence
people.cs.pitt.edu“The branch of computer science that is concerned with the automation of in-telligent behavior” (Luger+Stubblefield, 1993) Views of AI fall into four categories: Thinking humanly Thinking rationally Acting humanly Acting rationally Examining these, we will plump for acting rationally (sort of) AIMA Chapter 1 (after Russell and Norvig) 3
Propositional logic: Horn clauses
people.cs.pitt.edu• Horn form (Horn normal form) • Two inference rules that are sound and complete with respect to propositional symbols for KBs in the Horn normal form: – Resolution (positive unit resolution) – Modus ponens (A∨¬B) ∧(¬A∨¬C ∨D) Can be written also as: (B ⇒ A) ∧(( A ∧C) ⇒ D) CS 2740 Knowledge Representation M. Hauskrecht ...
Time Series: Autoregressive models AR, MA, ARMA, ARIMA
people.cs.pitt.eduGaussian White Noise {A particular useful white noise is Gaussian white noise, wherein the w ... -20 0 20 40 60 80 12/77. Time Series Analysis The procedure of using known data values to t a time series ... Measures of Dependence A complete description of a time series, observed as a
Introduction to Kernel Methods
people.cs.pitt.edu1 Introduction to Kernel Methods Dave Krebs CS 3750 Fall 2007 ... Paradigm for Pattern Analysis. Kernel Methods in Bioengineering, Signal and Image Processing. 2007. ... 9 Mercer’s Condition (continued) if and only if, for any g(x) such that is finite, then It can be ...
Probabilities: Expected value
people.cs.pitt.eduExpected value Investment problem: • You have 100 dollars and can invest into a stock. The returns are volatile and you may get either $120 with probability of 0.4, or $90 with probability 0.6. • What is the expected value of your investment? • M. Hauskrecht Expected value Investment problem: • You have 100 dollars and can invest into a ...
Sets and set operations - University of Pittsburgh
people.cs.pitt.edu• Ordered-n tuples are used to represent an ordered collection. Definition: An ordered n-tuple (x1, x2, ..., xN) is the ordered collection that has x1 as its first element, x2 as its second element, ..., and xN as its N-th element, N 2. Example: • Coordinates of a point in the 2-D plane (12, 16) x y
Mathematical induction & Recursion
people.cs.pitt.eduMathematical induction • Used to prove statements of the form x P(x) where x Z+ Mathematical induction proofs consists of two steps: 1) Basis: The proposition P(1) is true. 2) Inductive Step: The implication P(n) P(n+1), is true for all positive n. • Therefore we conclude x P(x).
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madasmaths.comMP2-X , r = ±2 3 Question 4 (***+) An arithmetic series has common difference 2. The 3rd, 6th and 10 th terms of the arithmetic series are the respective first three terms of a geometric series. Determine in any order the first term of the arithmetic series and the common ratio of the geometric series. MP2-Z , a =14 , 4 3 r =
SEQUENCES AND SERIES
ncert.nic.in9.2 Sequences Let us consider the following examples: Assume that there is a generation gap of 30 years, we are asked to find the number of ancestors, i.e., parents, grandparents, great grandparents, etc. that a person might have over 300 years. Here, the total number of generations = 300 10 30 = Fibonacci (1175-1250) Chapter SEQUENCES AND SERIES 9
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www.bath.k12.ky.us©p V2v0X1L3r TKEu etAai ZS3oYfthw0aur je b 3LYLlCD.O o 2A Il 2l M YrUiVgAh0tcse rzews Ee Ir Gvue Bdt. 9 4.3 Arithmetic and Geometric Sequences Worksheet Determine if the sequence is arithmetic. If it is, find the common difference. 1) −9, −109 , −209 , −309 , ... d = −100 2) 28 , 18 , 8, −2, ... d = −10 3) 28 , 26 , 24 , 22 , ...
Arithmetic and Geometric Sequences Worksheet
www.crsd.org4. For the following geometric sequences, find a and r and state the formula for the general term. a) 1, 3, 9, 27, ... b) 12, 6, 3, 1.5, ... c) 9, -3, 1, ... 5. Use your formula from question 4c) to find the values of the t 4 and t 12 6. Find the number of terms in the following arithmetic sequences. Hint: you will need to find the formula for ...