Basic Probability Notes Probability— the relative frequency or likelihood that a specific event will occur. If the event is A‚ then the probability that A will occur is denoted P(A). Example: Flip a coin. What is the probability of heads? This is denoted P(heads). Properties of Probability 1. The probability of an event E always lies in the range of 0 to 1; i.e.‚ 0 ≤ P( E ) ≤ 1. Impossible event—an event that absolutely cannot occur; probability is zero. Example: Suppose you roll a normal die
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Chapter 1 The Probability in Everyday Life In This Chapter Recognizing the prevalence and impact of probability in your everyday life Taking different approaches to finding probabilities Steering clear of common probability misconceptions You’ve heard it‚ thought it‚ and said it before: “What are the odds of that happening?” Someone wins the lottery not once‚ but twice. You accidentally run into a friend you haven’t seen since high school during a vacation in Florida. A cop pulls you over the
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QMT200 CHAPTER 3: PROBABILITY DISTRIBUTION 3.1 RANDOM VARIABLES AND PROBABILITY DISTRIBUTION Random variables is a quantity resulting from an experiment that‚ by chance‚ can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable. 3.2 DISCRETE RANDOM VARIABLE A random variable is called
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The North Star Concert North Star.xls Best Guess‚ Worst Case‚ Best Case; and Continuous Uncertainties 3 Engine Services‚ Inc. Quick Start Guide to Crystal Ball Analyzing Uncertainty‚ Probability Distributions‚ and Simulation Learning Module: Crystal Ball Litigate Demo Engine Services.xls Language of Probability Distributions and Monte Carlo Simulation 4 Taurus Telecommunications Corporation: A New Prepaid Phone Card Learning Module: Tornado Sensitivity Taurus Telecommunications.xls Sensitivity
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PROBABILITY and MENDELIAN GENETICS LAB Hypothesis: If we toss the coin(s) for many times‚ then we will have more chances to reach the prediction that we expect based on the principle of probability. Results: As for part 1: probability of the occurrence of a single event‚ the deviation of heads and tails of 20 tosses is zero‚ which means that the possibility of heads and tails is ten to ten‚ which means equally chances. The deviation of heads and tails of 30 tosses is 4‚ which means that the
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cutting a deck of cards for $1‚000. What is the probability that the card for the gambler will be the following? a. A face card – there are 12 face cards in a deck of 52 cards. The probability would be 12/52 b. A queen – there are 4 queens in a deck‚ so the probability would be 4/52 c. A Spade - There are 13 cards of each suit so the probability is 13/52 or ¼. d. A jack of spades - There is only 1 jack of spades in a deck‚ so the probability would be 1/52 2. The employees in the textile
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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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Factor of safety and probability of failure Introduction How does one assess the acceptability of an engineering design? Relying on judgement alone can lead to one of the two extremes illustrated in Figure 1. The first case is economically unacceptable while the example illustrated in the drawing on the right violates all normal safety standards. Sensitivity studies The classical approach used in designing engineering structures is to consider the relationship between the capacity C (strength
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1/08/13 Probability Primer Principles of Econometrics‚ 4th Edition Probability Primer Page 1 ! Announcement: ! Please make sure you know who your tutor is and remember their names. This will save confusion and embarrassment later. ! Kai Du (David) ! Ngoc Thien Anh Pham (Anh) ! Zara Bomi Shroff Principles of Econometrics‚ 4th Edition Probability Primer Page 2 Chapter Contents ¡ P.1 Random Variables ¡ P.2 Probability Distributions ¡ P.3 Joint
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variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations‚ which gives each observation equal weight‚ the mean of a random variable weights each outcome xi according to its probability‚ pi. The mean also of a random variable provides the long-run average of the variable‚ or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is ‚ formally defined by Variance
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