PROBABILITY P(A U B)= P(A) + P(B) – P(A∩B) If P(A∩B) = 0 then A and B are mutually exclusive and P(AUB) = P(A) + P(B) Joint Probability Marginal Probability PXY(x‚y) = P(X=x ∩ Y=y) PX(x) = ∑P(X=x ∩ Y=y) (For all values of y) Quotient Rule: Multiplication Rule P(A|B) = P(A∩B) / P(B) P(A∩B) = P(A|B) x P(B) = P(B|A) x P(A) Two events are statistically independent if: P(A|B) = P(A) P(B|A) = P(B) P(A∩B) = P(A) P(B) _ _ P(A) = P(A|B)P(B) + P(A|B)P(B) Bayes Rule:
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Contents Preface 1 Quantitative Methods: Should We Bother? 1.1 Solutions 1.2 Computational supplements 1.2.1 Optimal mix problem Calculus 2.1 Solutions Linear Algebra 3.1 Solutions Descriptive Statistics: On the Way to Elementary Probability 4.1 Solutions Probability Theories 5.1 Solutions 5.2 Additional problems 5.3 Solutions of additional problems Discrete Random Variables 6.1 Solutions vii 1 1 3 3 7 7 15 15 25 25 29 29 30 31 33 33 v 2 3 4 5 6 vi CONTENTS 7 Continuous
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DISTRIBUTIONS I. Concept of probability (3%) 1. Explain why the distribution B(n‚p) can be approximated by Poisson distribution with parameter if n tends to infinity‚ p 0‚ and = np can be considered constant. 2. Show that – and + are the turning points in the graph of the p.d.f. of normal distribution with mean and standard deviation . 3. What is the relationship between exponential distribution and Poisson distribution? II. Computation of probability (7%) 1. Let
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CHAPTER 3 ASSIGNMENT DESCRIBING DATA: NUMERICAL MEASURES Part I Select the correct answer and write the appropriate letter in the space provided. c 1. The arithmetic mean is computed by a. finding the value that occurs most often. b. finding the middle observation and dividing by 2. c. summing the values and dividing by the number of values. d. selecting the value in the middle of the data set. c 2. To compute the arithmetic mean at least the a. nominal level of measurement is required
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As a storm approaches‚ Mr. Jaeger must evaluate the risk of harvesting his Riesling grapes immediately or holding off and taking the chance the grapes become thin or produce no mold and sell at a lower price. Mr. Jaeger must evaluate the risk and the expected revenues related to his different options. The recommendation is that Mr. Jaeger should not harvest the Riesling grapes right now but wait for a better profit given by the possibility of an upcoming rainstorm that may prove to produce a botrytis
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year. (a) Find the mean waiting time between accidents. (b) Find the standard deviation of the waiting times between accidents. (c) Find the probability that more than one year elapses between accidents. (d) Find the probability that less than one month elapses between accidents. (e) If no accidents have occurred within the last six months‚ what is the probability that an accident will occur within the next year? Question 4: [20 points] If T is a continuous random
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Basic Skills in Statistics A Guide for Healthcare Professionals Adrian Cook Gopalakrishnan Netuveli and Aziz Sheikh “The authors are to be congratulated for providing non-experts with such a clear introduction to statistics.” From the Foreword by Professor Philip Hannaford‚ University of Aberdeen Comments on Basic Skills in Statistics: A Guide for Healthcare Professionals from readers ‘This publication is a fantastic resource for any health professional with an interest in research and
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finding strategies for several different probability games. The key ideas were developed in the unit through the presentation of many games and variations of those games to us. The key ideas helped us to solve the central problem by giving us many opportunities to learn how to solve strategies for probability games. In each different game there was a new game or variation in which we could find a new way to find optimal game strategies for probability games. Why I chose each item: Homework
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Statistics - Statistics is the science of collecting organizing‚ presenting‚ analyzing and interpreting data. It turns Data into information through transformation. Population ! - Everyone in group ! ! - µ is the mean ! - σ is the standard deviation Sample! - Some/Portion of group ! -x is the mean!! -S is the standard deviation Measurement Scales Types of Data Categorical/Qualitative Categorical/Qualitative Nominal! -Data has category but no order Data that can only be in categories
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APStatistics Statistics Assignment 12: Rules of Probability Directions: Complete the assignment on your own paper. Clearly label each answer. (34 points) 1. You roll a pair of standard dice. Create the sample space for a single roll of the dice and use the sample space to compute the following probabilities. (8 points) a. Create a sample space. {1‚ 2‚ 3‚ 4‚ 5‚ 6} b. P (getting a 1 on the first die or getting a 6 on the second die) 1/6+1/6= .333 c. P (getting a 3 on the second die given that
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