skills can be used anytime and anywhere. For instance‚ the mathematical usage of probability can aid people in smart decision making‚ and can help people understand their odds. Statistically‚ probability refers to the relative possibility that an event will occur‚ as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences (SOURCE). A rather obvious activity where probability applies is to is gambling. Casino games‚ such as Texas Hold Em’‚ can be played
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Chapter 2—Introduction to Probability PROBLEM 1. A market study taken at a local sporting goods store showed that of 20 people questioned‚ 6 owned tents‚ 10 owned sleeping bags‚ 8 owned camping stoves‚ 4 owned both tents and camping stoves‚ and 4 owned both sleeping bags and camping stoves. Let: Event A = owns a tent Event B = owns a sleeping bag Event C = owns a camping stove and let the sample space be the 20 people questioned. a. Find P(A)‚ P(B)‚ P(C)‚ P(A C)‚ P(B C). b
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Bayesian Probabilistic Matrix Factorization using Markov Chain Monte Carlo Ruslan Salakhutdinov rsalakhu@cs.toronto.edu Andriy Mnih amnih@cs.toronto.edu Department of Computer Science‚ University of Toronto‚ Toronto‚ Ontario M5S 3G4‚ Canada Abstract Low-rank matrix approximation methods provide one of the simplest and most effective approaches to collaborative filtering. Such models are usually fitted to data by finding a MAP estimate of the model parameters‚ a procedure that can be
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RISK THEORY - LECTURE NOTES 1. INTRODUCTION The primary subject of Risk Theory is the development and study of mathematical and statistical models to describe and predict the behaviour of insurance portfolios‚ which are simply financial instruments composed of a (possibly quite large) number of individual policies. For the purposes of this course‚ we will define a policy as a random (or stochastic) process generating a deterministic income in the form of periodic premiums‚ and incurring financial
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Tutorial on Discrete Probability Distributions Tutorial on discrete probability distributions with examples and detailed solutions. ------------------------------------------------- Top of Form | Web | www.analyzemath.com | | Bottom of Form | | Let X be a random variable that takes the numerical values X1‚ X2‚ ...‚ Xn with probablities p(X1)‚ p(X2)‚ ...‚ p(Xn) respectively. A discrete probability distribution consists of the values of the random variable X and their corresponding
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product of the twentieth century. Decision analysis refers to a body of techniques that allows a decision-maker to evaluate uncertainty‚ risk‚ and multiple objectives decision problems. Among the topics that will be covered in this course are decision theory‚ forecasting‚ linear programming‚ transportation and assignment models‚ waiting line analysis‚ simulation‚ network flow models and project management. 2. LEARNING OUTCOMES 1. To develop a conceptual understanding of commonly applied
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Chapter 3 Probability Distributions 1. Based on recent records‚ the manager of a car painting center has determined the following probability distribution for the number of customers per day. Suppose the center has the capacity to serve two customers per day. |x |P(X = x) | |0 |0.05 | |1 |0.20 | |2 |0.30 | |3 |0.25 | |4 |0.15 | |5 |0.05 | a. What is the probability that one
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QUEUING THEORY INTRODUCTION Waiting lines are the most frequently encountered problems in everyday life. For example‚ queue at a cafeteria‚ library‚ bank‚ etc. Common to all of these cases are the arrivals of objects requiring service and the attendant delays when the service mechanism is busy. Waiting lines cannot be eliminated completely‚ but suitable techniques can be used to reduce the waiting time of an object in the system. A long waiting line may result in loss of customers to an organization
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Model with Poisson Arrivals and Exponential Service Times Multiple-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times Economic Analysis of Waiting Lines Slide 1 Structure of a Waiting Line System Queuing theory is the study of waiting lines. Four characteristics of a queuing system are: •the manner in which customers arrive •the time required for service •the priority determining the order of service •the number and configuration of servers in the
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ETM2126: INFORMATION THEORY & ERROR CODING Tutorial 2 Tutorial 2: Channel Capacity 1. Two identical binary symmetric channels with transition probability p are connected in cascade. i) Draw the original channel diagram. ii) Find the overall channel matrix of the resultant channel and then draw the equivalent channel diagram. 2. Find the value of conditional entropy for a noiseless binary channel. 3. A telephone line channel has a bandwidth of 3 kHz and a S/N
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