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Probabilities: Expected value
Probabilities: Expected value M. Hauskrecht Probability basics Sample space S: space of all possible outcomes Event E: a subset of outcomes Probability: a number in [0,1] we can associate with an an outcome or an event Probability distribution A function p: S [0,1] that assigns a probability to every possible outcome in S L ' L Í L : O ; ∈ ...
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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
people.cs.pitt.edu11/9/2011 1 MIPS Floating Point Instructions CS/COE 447 Why Floating Point? • Sometimes need very small, or very large numbers? Non-integers?
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 ...
Sequences and summations
people.cs.pitt.eduSequences and summations CS 441 Discrete mathematics for CS M ... Arithmetic progression Definition: An arithmetic progression is a sequence of the ... -1, 3, 7, 11, … 3 CS 441 Discrete mathematics for CS M. Hauskrecht Geometric progression Definition A geometric progression is a sequence of the form: a, ar, ar2, ..., ark, where a is the ...
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 ...
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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CHAPTER 2 Estimating Probabilities
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RELEVANT PERCENTAGES FOR BRIDGE PLAYERS
www.bridgewebs.comThe percentages for card division presume that there is NO evidence from bidding or play to alter the probabilities. Eg a hand which has pre-empted showing a 7 card club suit has only 6 ‘vacant spaces’ for other cards while if declarer and dummy together have 4 clubs the other defender has 2 clubs leaving 11 vacant spaces in that hand.
Risk-Neutral Probabilities
people.stern.nyu.eduRisk-Neutral Probabilities 6 Examples of Risk-Neutral Pricing With the risk-neutral probabilities, the price of an asset is its expected payoff multiplied by the riskless zero price, i.e., discounted at the riskless rate: call option: Class Problem: Price the put option with payoffs K u =2.71 and K d =0 using the risk-neutral probabilities. €
Predicting Good Probabilities With Supervised Learning
www.cs.cornell.eduPredicting Good Probabilities With Supervised Learning also justified for boosted trees and boosted stumps. Let the output of a learning method be f(x). To get cali-brated probabilities, pass the output through a sigmoid: P(y = 1jf) = 1 1+exp(Af +B) (1) where the parameters A and B are fitted using maximum
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Tabl e: Cumulative Binomial probabilities [ ] n ( ) P X c ...
www.math.hawaii.eduTable: Cumulative Binomial probabilities ( continued ) 2 p c 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95
15 Markov Chains: Limiting Probabilities
www.math.ucdavis.edu15 MARKOV CHAINS: LIMITING PROBABILITIES 170 This is an irreducible chain, with invariant distribution π0 = π1 = π2 = 1 3 (as it is very easy to check). Moreover P2 = 0 0 1 1 0 0 0 1 0 , P3 = I, P4 = P, etc. Although the chain does spend 1/3 of the time at each state, the transition
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www.princeton.eduPredicted probabilities after logit/probit: estimating the probability that the outcome variable = 1, setting a predictor to specific value