Basic Probability Notes Probability— the relative frequency or likelihood that a specific event will occur. If the event is A‚ then the probability that A will occur is denoted P(A). Example: Flip a coin. What is the probability of heads? This is denoted P(heads). Properties of Probability 1. The probability of an event E always lies in the range of 0 to 1; i.e.‚ 0 ≤ P( E ) ≤ 1. Impossible event—an event that absolutely cannot occur; probability is zero. Example: Suppose you roll a normal die
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Conditional Probability How to handle Dependent Events Life is full of random events! You need to get a "feel" for them to be a smart and successful person. Independent Events Events can be "Independent"‚ meaning each event is not affected by any other events. Example: Tossing a coin. Each toss of a coin is a perfect isolated thing. What it did in the past will not affect the current toss. The chance is simply 1-in-2‚ or 50%‚ just like ANY toss of the coin. So each toss is an Independent
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Bayes’ theorem describes the relationships that exist within an array of simple and conditional probabilities. For example: Suppose there is a certain disease randomly found in one-half of one percent (.005) of the general population. A certain clinical blood test is 99 percent (.99) effective in detecting the presence of this disease; that is‚ it will yield an accurate positive result in 99 percent of the cases where the disease is actually present. But it also yields false-positive results in 5
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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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Probability Paper David E. Nelson QNT/561 February 14‚ 2013 Professor Minh Bui Probability Paper My friends suggested that we take a hiking trip through South America this year. The reason for such a trip was to celebrate 16 years of close friendship. The four of us had known each other since we were in middle school and have since become inseparable. Even though we all lead very different lives and have even started our own families‚ we always manage to find time to spend with each other
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Introduction Objectives PROBABILITY 2.2 Some Elementary Theorems 2.3 General Addition Rule 2.4 Conditional Probability and Independence 2.4.1 Conditional Probability 2.4.2 Independent Events and MultiplicationRule 2.4.3 Theorem of Total Probability and Bayes Theorem 2.5 Summary 2.1 INTRODUCTION You have already learnt about probability axioms and ways to evaluate probability of events in some simple cases. In this unit‚ we discuss ways to evaluate the probability of combination of events
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CONDITIONAL TENSE Conditional sentences usually are of the type in which one circumstance will be symbiotic with the other. For example‚ “if I find her address‚ I’ll send her the invite.” Normally‚ there are three kinds of relationships which can be expressed using the conditional- factual‚ future‚ and imaginative conditional relationship. Factual conditionals generate two branches- timeless and time-bound conditionals. Furthermore‚ timeless conditionals are divided into habitual and generic
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Teaching ideas for first conditional Maja Hadzic‚ Belgrade‚ Serbia 1. I usually give some examples of superstitions‚ e.g. If you break a mirror‚ you will... (they give the answer‚ since they already know Future Simple Tense). 2. Then I give some more oral examples for them to finish. 3. After that they make their own examples. 4. Now they write down an example or two. 5. In groups they try to figure out what goes with the IF clause‚ what with the main clause. They report back to the class
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guys‚ this is the probability Assignment. Last date for submission is 10 aug... Q1. What is the probability of picking a card that was either red or black? Q2. A problem in statistics is given to 5 students A‚ B‚ C‚ D‚ E. Their chances of solving it are ½‚1/3‚1/4‚1/5‚1/6. What is the probability that the problem will be solved? Q3. A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit the target in 2 out of 3 shots. Find the probability that the target
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Probability 1.) AE-2 List the enduring understandings for a content-area unit to be implemented over a three- to five- week time period. Explain how the enduring understandings serve to contextualize (add context or way of thinking to) the content-area standards. Unit: Data and Probability Time: 3 weeks max Enduring Understanding: “Student Will Be Able To: - Know what probability is (chance‚ fairness‚ a way to observe our random world‚ the different representations) - Know what the
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