EE 562a: Random Processes in Engineering EE department‚ USC‚ Fall 2014 Instructor: Prof. Salman Avestimehr Homework 1 Solutions 1. (Axioms of Probability) Prove the union bound: n P [∪n Ak ] ≤ k=1 P [Aj ]. j=1 The union bound is useful because it does not require that the events Aj be independent or disjoint. Problem 1 Solution We prove this part by induction‚ for k = 2 we have P (A1 ∪ A2 ) = P (A1 ) + P (A2 ) − P (A1 ∩ A2 ) ≤ P (A1 ) + P (A2 ) (1) Now‚ assume that
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below it is clear to see that Outcome Node #1 (new product‚ thorough development) has the highest total value‚ at $210‚200‚ across the range of uncertain market outcomes. This is from summing the predicted gains as modified their differential probabilities. #1 New Product‚ Thorough Development P Mkt Reaction Predicted Gains VALUE 0.4 Good $500‚000 $200‚000 0.4 Moderate $25‚000 $10‚000 0.2 Poor $1‚000 $200 TOTAL $210‚200 #2 New Product‚ Rapid Development P Mkt
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Cable TV Networks Regulation Act in 1995 was a hurriedly drafted Bill and lacked several important elements. The Cable TV consumer rates have gone up 30-40 per cent whereas the inflation is only about 2 per cent. The Amendment Bill‚ called the Conditional Access System Bill‚ was introduced to keep some check on the regularly escalating cable subscription rates. Though this solution could hardly be called effective‚ at least it gave the government a means to keep tabs on the premium tier. Though the
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GVPT 377 Thought Piece 1 Jimmy Duffy 5/1/2012 The Social Compact and its Influence on the American Cause “But when a long train of abuses and usurpations‚ pursuing invariably the same Object evinces a design to reduce them under absolute Despotism‚ it is their right‚ it is their duty‚ to throw off such Government‚ and to provide new Guards for their future security. — Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to
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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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respectively. The probability a “good” driver will have an accident is .01‚ the probability a “medium” risk driver will have an accident is .03‚ and the probability a “poor” driver will have an accident is .10. The company sells Mr. Brophy an insurance policy and he has an accident. What is the probability Mr. Brophy is: a. A “good” driver? (Round your answers to 3 decimal places.) Probability b. A “medium” risk driver? (Round your answers to 3 decimal places.) Probability c. A “poor”
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Section 3.1‚ Exercise #14‚ p. 125 Finding Probabilities consider a company that selects employees for random drug tests. The company uses a computer to select randomly employee numbers that range from 1 to 6296. Find the probability of selecting a number greater than 1000. P(E) = Number of outcomes in E / Total number of Outcomes in sample space Number of outcomes in E = 6296 – 100 = 5296 The probability = P(E) = 5296 / 6296 = 0.841 = 84.1%
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and also satisfy yourself that you are also comfortable with the worked examples provided on this topic in the lecture materials. See your lecturer‚ tutor or the Student Learning Unit for assistance with any of this material. Introduction to Probability A market research firm‚ interested in investigating the relationship between the ability of the consumer to recall a television commercial for a particular product and the actual purchase of the product‚ conducted a survey of 800 people. The responses
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dont les marges sont donnes. Annales de l’ Giddens‚ A. (2006). Sociology (5 ed.). Polity Press. Hild‚ M. and A. Voorhoeve (2004). Equality of opportunity and opportunity dominance. Economics and Philosophy 20‚ 117– Hogg‚ R. and E. Tanis (1997). Probability and statistical inference. Prentice Hall. Hutchens‚ R. (2001). Numerical measures of segregation: desirable properties and their implications. Mathematical Social Sciences 42‚ 13– 29. James‚ D. and K. Taeuber (1985). Measures of segregation. Sociological
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is the probability that it will rain on the day of my daughter’s birthday party given the current weather forecast. The April average for total rainfall plus snowfall in Middletown‚ CT is eleven days( n.d.) An extended (10 day) weather forecast shows a 40% chance of rain on April 9‚ 2011 ( n.d.). According to the National Oceanic and Atmospheric Administration (NOAA)‚ the accuracy of 6-10 day precipitation forecasts for the continuous United States stands at 40%. Using probability statistical
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