numbers that could be delivered. __T__ 6. When assigning subjective probabilities‚ use experience‚ intuition‚ and any available data. __F__ 7. P (AxB) d P (A) __F__ 8. If P (A|B) = .4 and P (B) = .6‚ then P (AxB) = .667. __T__ 9. Bayes’ theorem provides a way to transform prior probabilities into posterior probabilities. __T__ 10. If P (AyB) = P (A) + P (B)‚ then A and B are mutually exclusive. Section B Multiple Choice Identify the letter of the choice that best completes the statement
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P(Unsuccessful venture | Unfav survey) = 0.6 Iverstine & Walker Probabilities P(Fav survey | Succes) = 0.9 P(Unfav survey | Success) = 0.1 P(Fav survey | Failure) = 0.2 P(Unfav survey | Failure) = 0.8 Calculations for Posterior Probabilities (Bayes Theorem) included in decision tree Posterior Probabilities for Iverstine & Walker if Survey is Favorable Outcome P(Fav survey | Outcome) Prior Probability Join Prob Posterior Joint Prob Equation Posterior Prob Equation
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5. Remainder Theroem 1. June 1986 Paper 2 #1 (16 marks) a) Find the remainder when x³ + 3x – 2 is divided by x + 2 [2] b) Find the value of a for which (1 – 2a) x² + 5ax + (a – 1)(a – 8) is divisible by x – 2 but not by x – 1. [7] c) Given that 16x4 – 4x³ – 4b²x² + 7bx + 18 is divisible by 2x + b‚ i) show that b³ – 7b² + 36 = 0 [3] ii) find the possible values of b [4] 2. June 1987 Paper 2 #1 (16 marks) a) Given that f(x) = x³ – 7x + 6 i) calculate the remainder when f(x) is divided by
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Throughout in this text V will be a vector space of finite dimension n over a field K and T : V → V will be a linear transformation. 1 Eigenvalues and Eigenvectors A scalar λ ∈ K is an eigenvalue of T if there is a nonzero v ∈ V such that T v = λv. In this case v is called an eigenvector of T corresponding to λ. Thus λ ∈ K is an eigenvalue of T if and only if ker(T − λI) = {0}‚ and any nonzero element of this subspace is an eigenvector of T corresponding to λ. Here I denotes the identity mapping
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ABC Auto Insurance classifies drivers as good‚ medium‚ or poor risks. Drivers who apply to them for insurance fall into these three groups in the proportions 30%‚ 50%‚ and 20%‚ respectively. The probability a “good” driver will have an accident is .01‚ the probability a “medium” risk driver will have an accident is .03‚ and the probability a “poor” driver will have an accident is .10. The company sells Mr. Brophy an insurance policy and he has an accident. What is the probability Mr. Brophy is:
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Unit 1 Lesson 1: Optimization with Parameters In this lesson we will review optimization in 2-space and the calculus concepts associated with it. Learning Objective: After completing this lesson‚ you will be able to model problems described in context and use calculus concepts to find associated maxima and minima using those models. You will be able to justify your results using calculus and interpret your results in real-world contexts. We will begin our review with a problem in which most
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International Journal of Computer Trends and Technology (IJCTT) – volume 7 number 1– Jan 2014 Early Proliferation Stage of Detecting Diabetic Retinopathy Using Bayesian Classifier Based Level Set Segmentation S.Vijayalakshmi1‚ P.Sivaprakasam2 1 (Research Scholar‚ Karpagam University‚Coimbatore‚ India) (Department of MCA‚ Park College of Engineering and Technology‚ Coimbatore‚ India) 2 (Department of Computer Science‚ Associate Professor Sri Vasavi College‚ Erode‚ India) 1 ABSTRACT
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Probability Introduction The probability of a specified event is the chance or likelihood that it will occur. There are several ways of viewing probability. One would be experimental in nature‚ where we repeatedly conduct an experiment. Suppose we flipped a coin over and over and over again and it came up heads about half of the time; we would expect that in the future whenever we flipped the coin it would turn up heads about half of the time. When a weather reporter says “there is a 10% chance
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Fault-Tolerant Observers Supervisor: Dr Imad M. Jaimoukha Designing of a robust fault-tolerant observer that guarantees a certain level of performance for real-time applications. By: YEO Zhi-Wei‚ Laurence 00566245 Overview For any system such as a factory plant‚ an aircraft jet engine system or a water pumping system‚ it can be replicatedi by a mathematical model which includes the affecting dynamics based on observations and assumptions. However‚ it would be practically challenging
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C H A P T E R 3 RESISTIVE NETWORK ANALYSIS hapter 3 illustrates the fundamental techniques for the analysis of resistive circuits. The chapter begins with the definition of network variables and of network analysis problems. Next‚ the two most widely applied methods— node analysis and mesh analysis—are introduced. These are the most generally applicable circuit solution techniques used to derive the equations of all electric circuits; their application to resistive circuits
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