the honor code pledge printed on your bluebook. No books‚ notes or electronic devices of any kind are allowed. Show all work‚ justify your answers. 1. (25 pts) Suppose events A‚ B and C‚ all defined on the same sample space‚ have the following probabilities: P(A) = 0.22‚ P(B) = 0.25‚ P(C) = 0.28‚ P(A ∩ B) = 0.11‚ P(A ∩ C) = 0.05‚ P(B ∩ C) = 0.07 and P(A ∩ B ∩ C) = 0.01. For each of the following parts‚ your answer should be in the form of a complete mathematical statement. (a) Let D be the event that
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Mean is the average of all the data. Mode is the number that occurs most frequently in the data set. Median is the middle value or average of the two middle values when the data is arranged in order from smallest to larges. Chapter 4: Basic Probability Concepts:In an organization of 30 people‚ we wish to elect 3 officers. How many different groups of officers are possible? 30*29*28=24‚360 (if only 1 person per office). Or 30*30*30=27‚000 (if 1 person can hold more than one office). Combinations:
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Notes 6 Statistics Continuous Probability Distributions Probability Density Function [f(x)] –area under the graph of f(x) gives probability Uniform Probability Distribution ! for a ≤ x ≤ b f(x) = !!! 0 elsewhere !!! (!!!)! E(x) = ! ‚ Var(x) = ! Normal Probability Distribution Most important continuous probability distribution Many applications: heights‚ weights‚ rainfall‚ test scores Used extensively in statistical inference Shape of normal distribution is bell-shaped
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evaluation phase‚ people behave as if they would compute a value (utility)‚ based on the potential outcomes and their respective probabilities‚ and then choose the alternative having a higher utility. The formula that Kahneman and Tversky assume for the evaluation phase is (in its simplest form) given by where are the potential outcomes and their respective probabilities. v is a so-called value function that assigns a value to an outcome. The value function (sketched in the Figure) which passes
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decision-maker to make decisions under risk or uncertainty. The concept of probability is fundamental to the use of the risk analysis techniques. Hoe is probability defined? How are probabilities estimated? How are they used in the risk analysis techniques? How do statistical techniques help in resolving the complex problem of analyzing risk in capital budgeting? We attempt to answer these questions in our posts. Probability defined The most crucial information for the capital budgeting decision
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decision tree we know that the decision to develop thoroughly has a probability of 0.4 in a good market and predicted gains of $500‚000. The second State of nature would be a moderate market reaction with a probability of .4 and predicted gains of $25‚000. The third state of nature is a poor market reaction with a probability of .2 with predicted gains of $1‚000. The expected monetary value (EMV) is determined by multiplying the probability in each state of nature by the predicted gains and then adding
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characteristics of either a sample or a population| ANS: B 3. How many simple random samples of size 3 can be selected from a population of size 7? a.|7| b.|21| c.|35| d.|343| ANS: C 4. Sampling distribution of is the a.|probability distribution of the sample mean| b.|probability distribution of the sample proportion| c.|mean of the sample| d.|mean of the population| ANS: A 5. A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation
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Conditional Probability Bayes’ Theorem Fall 2014 EAS 305 Lecture Notes Prof. Jun Zhuang University at Buffalo‚ State University of New York September 10‚ ... 2014 Prof. Jun Zhuang Fall 2014 EAS 305 Lecture Notes Page 1 of 26 Conditional Probability Bayes’ Theorem Agenda 1 Conditional Probability Definition and Properties Independence General Definition 2 Bayes’ Theorem Partition Theorem Examples Prof. Jun Zhuang Fall 2014 EAS 305 Lecture Notes Page
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Basic Business Statistics 12th Edition Chapter 5 Discrete Probability Distributions Copyright ©2012 Pearson Education‚ Inc. publishing as Prentice Hall Chap 5-1 Learning Objectives In this chapter‚ you learn: The properties of a probability distribution To compute the expected value and variance of a probability distribution To calculate the covariance and understand its use in finance To compute probabilities from binomial‚ hypergeometric‚ and Poisson distributions How to use
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analysis of the problem calls for an ideal demand order quantity situation with lower probability of stock-out option. Following is the statistical information given: The cost of goods sold per unit = $ 16 The cost of Sales price Per Unit = $ 24 Surplus inventory sales price per unit = $ 5 Cost of excess inventory per unit = $ 16- $ 5 = $ 11 Expected Demand predicted by Sales Forecaster= 20‚000 units Probability of demand between 10‚000 units and 30‚000 units = 0.95 Solution of the problem: In
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