T is a continuous random variable with probability density function (p.d.f.) f (t) and cumulative distribution function (c.d.f.) F (t) = Pr{T < t}‚ giving the probability that the event has occurred by duration t. G. Rodr´ıguez. Revised September‚ 2010 2 CHAPTER 7. SURVIVAL MODELS It will often be convenient to work with the complement of the c.d.f‚ the survival function ∞ S(t) = Pr{T ≥ t} = 1 − F (t) = f (x)dx‚ (7.1) t which gives the probability of being alive just before duration t‚ or
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coined the term probability‚ or probabilis? (Latin: probabilis credible) Cicero’s principal legacy in the field of randomness is the term he used‚ probabilis‚ which is the origin of the term we employ today. But it is one part of the Roman code of law‚ the Digest‚ compiled by Emperor Justinian in the sixth century‚ that is the first document in which probability appears as an everyday term of art 2. What is the rule for compounding probabilities? How to compute probability that one event and
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signifies a decision point; each alternative is followed by a circular node from which branches on the tree represent the possible outcomes or states of nature which could result. Strictly speaking‚ a decision tree must contain both probabilities of outcomes and conditional monetary values of those outcomes so that expected values can be computed. Let us apply the decision tree in an investment problem. Suppose we are to decide whether to invest our $1000 in stocks or to deposit it in our savings
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a coin randomly from your pocket‚ what is the probability that: a. You will draw a nickel? The probability of someone drawing a dime would be 4/11 or 36%. b. You will draw a dime? The probability of some drawing a nickel would be 6/11 or 54% c. You will draw a quarter? The probability of someone drawing a quarter would be 4/11 or 36% 2. You are rolling a pair of dice‚ one red and one green. What is the probability of the
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CHAPTER 1 Individuals are the objects described by a set of data. Individuals may be people‚ but they may also be animals or things. A variable is any change of an individual. A variable can take different values for different individuals. A categorical variable places an individual into one of several groups or categories. A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense. The distribution of a variable tells us what values
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and Oakes‚ D. Analysis of Survival Data‚ Chapman and Hall‚ (1984). [4] Dall’Aglio‚ G.‚ Frechet Classes and Compatibility of Distribution Functions‚ Symp. Math.‚ 9‚ (1972)‚ pp [5] Delianedis‚ G. and R. Geske‚ Credit Risk and Risk Neutral Default Probabilities: Information about Rating Migrations and Defaults‚ Working paper‚ The Anderson School at UCLA‚ (1998). [6] Duffie‚ D. and Singleton‚ K. Modeling Term Structure of Defaultable Bonds‚ Working paper‚ Graduate School of Business‚ Stanford University
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5.23 The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .18. The probability that a student has both cards is .03. (a) Find the probability that a student has either a Visa card or a MasterCard. (b) In this problem‚ are V and M independent? Explain. Problem 5.27 (page 197) 5.27 A survey of 156 introductory statistics students showed the following contingency table. Find each event probability. [pic] WebSurvey
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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level and Advanced Level Advanced International Certificate of Education MATHEMATICS STATISTICS Paper 6 Probability & Statistics 1 (S1) May/June 2004 1 hour 15 minutes Additional materials: Answer Booklet/Paper Graph paper List of Formulae (MF9) 9709/06 0390/06 READ THESE INSTRUCTIONS FIRST If you have been given an Answer Booklet‚ follow the instructions on the front cover of the Booklet
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Problems (f) This assignment is a sampling of question types. Preparation for Test #2 should include all questions provided to you (i.e. class examples‚ Practice Problems‚ Practice Test and this assignment). (g) Remember that Test#2 will include (1) Probability material‚ including (2) Binomial Distribution and (3) one Calculus question. Questions: 1. The following table gives the results of a survey of 900 movie goers in a particular city‚ their gender‚ age and preference for film-genre. Age (years)
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ISDS 361A Study Guide Chapter 7 * Discrete Random Variable = can take countable number of values / Continous = values are uncountable * Probability distribution: a table‚ a formula‚ or graph that describes the values of a random variable and the probability associated with these values. * Requirements of Probabilities P(x) = 1 ; Prob must lie between 0 and 1 * Population Mean = E(x) = (x)P(x) Population Variance =( x to the second power)P(x) – Mean squared * Standard Deviation
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