PROBABILITY DISTRIBUTION In the world of statistics‚ we are introduced to the concept of probability. On page 146 of our text‚ it defines probability as "a value between zero and one‚ inclusive‚ describing the relative possibility (chance or likelihood) an event will occur" (Lind‚ 2012). When we think about how much this concept pops up within our daily lives‚ we might be shocked to find the results. Oftentimes‚ we do not think in these terms‚ but imagine what the probability of us getting behind
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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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Subject CT3 Probability and Mathematical Statistics Core Technical Syllabus for the 2014 exams 1 June 2013 Subject CT3 – Probability and Mathematical Statistics Core Technical Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in the aspects of statistics and in particular statistical modelling that are of relevance to actuarial work. Links to other subjects Subjects CT4 – Models and CT6 – Statistical Methods: use the statistical concepts
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Technology & Science‚ Pilani Work-Integrated Learning Programmes Division Second Semester 2010-2011 Course Handout Course Number Course Title : AAOC ZC111 : Probability and Statistics Course E-mail address : aaoczc111@dlpd.bits-pilani.ac.in Course Description Probability spaces; conditional probability and independence; random variables and probability distributions; marginal and conditional distributions; independent random variables‚ mathematical exceptions‚ mean and variance‚ Binomial Poisson and normal
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Probability Concepts 1. Fundamental Concepts of Probability 2. Mutually Exclusive and Collectively Exhaustive 3. Statistically Independent and Dependent Events 4. Bayes’Theorem Learning Objectives • Understand the basic foundations of probability analysis • Learn the probability rules for conditional probability and joint probability • Use Bayes’ theorem to establish posterior probabilities Reference: Text Chapter 2 Introduction • Life is uncertain; we are note sure what the
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Probable Probability; Rolling Dice Statistics is based upon based upon common sense and logic‚ in a complex data. Probability is just one of the many topics in statistical mathematics. It is used in our daily life‚ all over the world. Even games‚ require taking a chance and using probability to determine the predicted outcomes. Probability is the measure of how often a particular event will happen if something is done repeatedly‚ (596 Webster’s Dictionary). You cannot determine
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consecutive points falling on one side of the centerline When the process is in statistical control‚ find the false alarm probability (Type-I error) for each case. The corresponding probability measures are obtained from the Normal table as P(3 " Z) = 0.00135 P(2 " Z) = 0.02275 P(1 " Z) = 0.1587 Solution: ! i) Use the Binomial distribution to ! calculate the probability measures. ! 3! 3! P(Y ! 2 n = 3‚ p = 0.02275) = (0.02275)2 (1" 0.02275) + (0.02275)3 = 0.00153 2!1! 3!0! Type-1
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random. What is the probability that at least one pair of shoes is obtained? 2. At a camera factory‚ an inspector checks 20 cameras and finds that three of them need adjustment before they can be shipped. Another employee carelessly mixes the cameras up so that no one knows which is which. Thus‚ the inspector must recheck the cameras one at a time until he locates all the bad ones. (a) What is the probability that no more than 17 cameras need to be rechecked? (b) What is the probability that exactly 17
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Use this probability to calculate the approximate number of packets containing no defective‚ one defective and two defective pens‚ respectively in a consignment of 20‚000 packets [ e^(--0.02) =0.9802 ] Ans. : 19604‚ 392‚ 3.92=4 respectively 2. A manufacturer who produces medicine bottles finds that 0.1% of the bottles are defective. The bottles are packed in the boxes of 500 bottles. A drug manufacturer buys 100 boxes from the producer of bottles . Using suitable probability distribution
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Chapter 3 Probability True/False 1. A contingency table is a tabular summary of probabilities concerning two sets of complementary events. Answer: True Difficulty: Medium 2. An event is a collection of sample space outcomes. Answer: True Difficulty: Easy 3. Two events are independent if the probability of one event is influenced by whether or not the other event occurs. Answer: False Difficulty: Medium 4. Mutually exclusive events have a nonempty
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