TEM1116 Probability and Statistics Tri1 2013/14 Chapter 1 Chapter 1: Discrete and Continuous Probability Distributions Section 1: Probability Contents: 1.1 1.2 1.3 1.4 1.5 Some basics of probability theory Axioms‚ Interpretations‚ and Properties of Probability Counting Techniques and Probability Conditional Probability Independence TEM1116 1 TEM1116 Probability and Statistics Tri1 2013/14 Chapter 1 1.1 Basics of Probability Theory Probability refers to the study
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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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point to another which sets the consistency of data distribution i. 5‚ 10‚ 15… ii. 30‚ 40‚ 50 d. Ratio – resembles similar characteristics with interval‚ except that there exists an ‘absolute zero-value’ June 4‚ 2013 MODULE 2: SAMPLE AND SAMPLING DISTRIBUTION Sample - any representation as a portion of the population this is used to conserve MET (money‚ effort‚ and time) Slovin’s Formula – used to determine the “ideal” sample size (n) Ex. N = 1000 e = 0.05
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or statement is true or false. __F__ 1. Two events that are independent cannot be mutually exclusive. __F__ 2. A joint probability can have a value greater than 1. __F__ 3. The intersection of A and Ac is the entire sample space. __T__ 4. If 50 of 250 people contacted make a donation to the city symphony‚ then the relative frequency method assigns a probability of .2 to the outcome of making a donation. __T__ 5. An automobile dealership is waiting to take delivery of nine new cars
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Question 1: discuss any five (5) common sampling techniques used in business research. Support you answer with relevant examples. Simple random sampling: The simple random sampling is one of the most widely-used random sampling method. The term “random” here does not mean a haphazard selection as many people think. The “random” in this method means each member of the population has equal opportunities being chosen be subject and no one in the identified population who could not be selected
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t) P (X > s + t) P (X > t) e−λ(s+t) e−λt e−λs P (X > s) – Example: Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes‚ λ = 1/10. What is the probability that a customer will spend more than 15 minutes in the bank? What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes? Solution: P (X > 15) = e−15λ = e−3/2 = 0.22 P (X > 15|X > 10) = P (X > 5) = e−1/2 =
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Karan negi 12.2 12.3 We use equation 2 to find out probability: F(t)=1 – e^-Lt 1-e^-(0.4167)(10) = 0.98 almost certainty. This shows that probability of another arrival in the next 10 minutes. Now we figure out how many customers actually arrive within those 10 minutes. If the mean is 0.4167‚ then 0.4167*10=4.2‚ and we can round that to 4. X-axis represents minutes (0-10) Y-axis represents number of people. We can conclude from this chart that the highest point with the most visitors
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True/False Questions 1. The standard deviation of any normal random variable is always equal to one. Answer: False Type: Concept Difficulty: Easy 2. For any normal random variable‚ the probability that the random variable will equal one is always zero. Answer: True Type: Concept Difficulty: Medium 3. The graph of a standard normal random variable is always symmetric. Answer: True Type: Concept Difficulty: Easy 4. The formula will convert any normal
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Tutorial on Discrete Probability Distributions Tutorial on discrete probability distributions with examples and detailed solutions. ------------------------------------------------- Top of Form | Web | www.analyzemath.com | | Bottom of Form | | Let X be a random variable that takes the numerical values X1‚ X2‚ ...‚ Xn with probablities p(X1)‚ p(X2)‚ ...‚ p(Xn) respectively. A discrete probability distribution consists of the values of the random variable X and their corresponding
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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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