Probability Theory and Game of Chance Jingjing Xu April 24‚ 2012 I. INTRODUCTION Probability theory is the mathematical foundation of statistics‚ and it can be applied to many areas requiring large data analysis. Curiously‚ that the study on probability theory has its root in parlor games and gambling. In 17th century‚ dice gambling was a very common entertainment among the upper class. An
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Mathematical Systems Probability Solutions by Bracket A First Course in Probability Chapter 4—Problems 4. Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a woman (for instance‚ X = 1 if the top-ranked person is female). Find P X = i ‚ i = 1‚ 2‚ 3‚ . . . ‚ 8‚ 9‚ 10. Let Ei be the event that the the ith scorer is female. Then the
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Probability 1.) AE-2 List the enduring understandings for a content-area unit to be implemented over a three- to five- week time period. Explain how the enduring understandings serve to contextualize (add context or way of thinking to) the content-area standards. Unit: Data and Probability Time: 3 weeks max Enduring Understanding: “Student Will Be Able To: - Know what probability is (chance‚ fairness‚ a way to observe our random world‚ the different representations) - Know what the
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uniformly distributed over (0‚ 10)‚ calculate the probability that a. X < 3 (Ans: 3/10) b. X > 6 (Ans: 4/10) c. 3 < X < 8. (Ans: 5/10) 2. Buses arrive at a specified stop at 15-minute intervals starting at 7 AM. That is‚ they arrive at 7‚ 7:15‚ 7:30‚ 7:45‚ and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:30‚ find the probability that he waits d. Less than 5 minutes for a
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1. A quality control engineer knows that 10% of the microprocessor chips produced by a machine are defective. Out of a large shipment‚ five chips are chosen at random. What is the probability that none of them is defective? What is the probability that at least one is defective? 2. An automated manufacturing process produces a component with an average width of 7.55 centimeters‚ with a standard deviation of 0.02 centimeter. All components deviating by more than 0.05 centimeter from the mean must
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APPLIED PROBABILITY AND STATISTICS APPLIED PROBABILITY AND STATISTICS DEPARTMENT OF COMPUTER SCIENCE DEPARTMENT OF COMPUTER SCIENCE STATISTICAL DISTRIBUTION STATISTICAL DISTRIBUTION SUBMITTED BY – PREETISH MISHRA (11BCE0386) NUPUR KHANNA (11BCE0254) SUBMITTED BY – PREETISH MISHRA (11BCE0386) NUPUR KHANNA (11BCE0254) SUBMITTED TO – PROFESSOR SUJATHA V. SUBMITTED TO – PROFESSOR SUJATHA V
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cloud or the probability that it will rain‚ we move from pure simulation to Monte Carlo. The reason for this distinction is that there may be other ways to define A that make it easier to estimate. This process is called variance reduction‚ since most of the error in A is statistical. Reducing the variance of A reduces the statistical error. We often have a choice between Monte Carlo and deterministic methods. For example‚ if X is a one dimensional random variable with probability density f (x)
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classical and empirical probabilities. a. Classical probabilities are based on assumptions; Empirical probabilities are based on observations. b. Classical probabilities do not require an action to take place; Empirical probabilities have to have been “performed”. 2) Gather 16 to 30 coins. Shake and empty bag of coins 10 times and tally up how many head and tails are showing. Number of coins: 20 * Consider the first toss‚ what is the observed probability of tossing a head? Of
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companies and the probability of getting a job offer there. These data are tabulated below. The tabulation is in the decreasing order of cost. 1. If the graduate applies to all 10 companies‚ what is the probability that she will get at least one offer? 2. If she can apply to only one company‚ base on cost and success probability criteria alone‚ should she apply to company 5? Why or why not? 3. If she applies to companies 2‚5‚8‚ and 9‚ what is the total cost? What is the probability that she will
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positions are filled at random form the 11 finalists‚ what is the probability of selecting: A: 3 females and 2 males? B: 4 females and 1 male? C: 5 females? D: At least 4 females? Problem 2 By examining the past driving records of drivers in a certain city‚ an insurance company has determined the following (empirical) probabilities: [pic] If a driver in this city is selected at random‚ what is the probability that: A: He or she drives less than 10‚000 miles per year or has
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