Eco-10026 Lecture6 2016.pdf

Eco-10026 Lecture6 2016.pdf - Lecture 6 Probability...

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Lecture 6: Probability Concepts Quantitative Methods 1: 1/25 ECO-10026 Quantitative Methods I Dr E. Symons R OOM DW 1.55, D ARWIN B UILDING e - mail: [email protected]
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Lecture 6: Probability Concepts Quantitative Methods 1: 2/25 Lecture Contents and Objectives Basic Probability concepts Describe the concept of Probability Compute simple Probabilities Characterise relationships between events and compute overall Probabilities Understand Conditional Probability Understand Marginal Probability Construct a Probability Tree Calculate Expected Values Decision models Reading Bradley Chaps 4&5, Swift and Piff Chap 10
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Lecture 6: Probability Concepts Quantitative Methods 1: 3/25 Defining Probability “Nothing in life is certain except death and taxes”, Benjamin Franklin Definition Probability is the likelihood or chance that a particular event will occur Probability enables us to make inferences about large populations from samples Defining Probability is not easy
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Lecture 6: Probability Concepts Quantitative Methods 1: 4/25 Terminology: A Statistical (or random) experiment refers to any process of observation that has more than one possible outcomes for which there is uncertainty about which outcome will actually happen E.g. tossing a coin, throwing a die... The set of all possible outcomes of an experiment is called Population or Sample Space E.g. tossing a ’fair’ coin: ({H}, {T});, tossing two ’fair’ coins: ({H, H}, {H, T}, { T , H}, { T , T}); throwing a ’fair’ die: ({1}, {2}, {3}, {4}, {5}, {6}) An Event is a particular collection of outcomes E.g. tossing two ’fair’ coins and obtain one Head: ({H, T}, {T, H}), throwing a ’fair’ die and obtain an odd number: ({1}, {3}, {5})
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Lecture 6: Probability Concepts Quantitative Methods 1: 5/25 The Classical Definition: Suppose we toss a “fair” coin. P(H) =? Suppose we throw a “fair” die. P(3)=?, Definition The probability of an event A to occur is: outcomes of number total A to favourable outcomes of no. P(A) P(H) = 1/2, P(3) = 1/6, P(odd) = 3/6 Disadvantages: We implicitly assume that each outcome is equally likely What if the coin is “unfair” so that P(H) = 0 Keele football society vs. Man.U?
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Lecture 6: Probability Concepts Quantitative Methods 1: 6/25 The Frequency Definition: To determine the Probability of an event A we repeat an experiment and count how many times event A occurs Definition The probability of an event A to occur is: conducted was experiment the times of number occurs A times of no.
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