Mathematics Department Tutorial Sheet No. 3 MAL250(Probability and Stochastic Processes) 1. The percentage of alcohol (100X ) in a certain compound may be considered as a random variable‚ where X (0 < X < 1) has pdf fX (x) = 20x3 (1 − x)‚ 0 < x < 1. Suppose that the selling price of the above compound depends on the alcohol contents. Specifically‚ if 1/3 < X < 2/3‚ the compound sells for c1 dollars/gallon otherwise it sells for c2 dollars/gallon. If the cost is c3 dollars/gallon‚ find the probability
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Introduction to Management Science‚ 10e (Taylor) Chapter 11 Probability and Statistics 1) Deterministic techniques assume that no uncertainty exists in model parameters. Answer: TRUE Diff: 1 Page Ref: 489 Main Heading: Types of Probability Key words: deterministic techniques 2) Probabilistic techniques assume that no uncertainty exists in model parameters. Answer: FALSE Diff: 1 Page Ref: 489 Main Heading: Types of Probability Key words: probabilistic techniques 3) Objective
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Spring 2013 BUAD 310 Applied Business Statistics F. Pereira Session 1 Introduction 1 Introduction Francis Pereira‚ Ph.D. Adjunct Professor Office : IOM 401J Office Hours: Wednesdays 1:00 – 2:00 PM and by appointment Telephone : (213) 821-1615 E-mail : pereira@marshall.usc.edu 2 Course Focus • Focus on learning various statistical techniques and their applications that will assist you in making business decisions. • Enable students to perform and understand statistical analysis of data‚ with
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Descriptive Statistics Kelly Calle QNT/561 February 15‚ 2015 John Carroll Descriptive Statistics and Interpretation Descriptive statistics is the term given to the analysis of data that helps describe‚ show‚ or summarize data in a meaningful way. Descriptive statistics does not allow conclusions beyond the data analyzed or reach conclusions regarding any hypotheses made. It is only a way to describe the data gathered. Descriptive statistics allows data to be presented in a more meaningful way
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these banks using the descriptive statistics feature. Study the output and describe what you can learn about the assets of these top 100 banks from the output. Top 100 Banks in the U.S Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 76.5411 17.93374 21.97 13.01 179.3374 32161.9 22.2632 4.586275 1096.01 8.99 1105 7654.11 100 PART B During the 1990s‚ businesses were expected to show a lot of interest in Central and Eastern
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the estimated model for stationarity. Question 3 A researcher is trying to determine the appropriate order of an ARMA model to describe some data‚ with 200 observations available. She has the following figures for the log of estimated residual variance (log(ˆ 2 )) for various candidate models. She has σ assumed that an order greater than (3‚3) should not be necessary to model the dynamics of the data. What is the “optimal” model order? ARMA(p‚ q) model order log(ˆ 2 ) σ (0‚0) 0.932 (1‚0) 0.864
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expected real returns you were getting earlier. If that is the case‚ use five expected real return levels that you can attain. viii) Compare the investment opportunities implied by part (vi) to those in part (vii). ix) Explain the pros of the mean variance paradigm. x) Explain the cons. I will describe how to perform portfolio optimization in class. Excel is equipped with an optimizer (Solver) that requires you to specify what you are trying to maximize or minimize‚ the variables (weights)
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The Probability of On-Base Percentage Affecting Total Team Wins I. Abstract In the baseball world‚ On-Base Percentage is the key element to a team’s advancement to post-season play‚ because offensive domination is essential to the desired outcome‚ namely‚ winning. The following will describe the relationship between On-Base Percentage and the total amount of wins a Major League Baseball team receives using a linear regression model and other descriptive graphs. II. Introduction Essentially
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Marked Problem Set 2 Dagoberto Gonzalez Paez Student ID --65824138 November 28‚ 2013 1. Suppose that you can trade a riskless asset that yields 5% and two risky assets A and B. The expected return of asset A is 8% and that of asset B is 11%‚ while the standard deviation of asset A is 14% and that of asset B is 23%. The covariance between assets A and B is ?0:0322. Solution . rA‚B= CovAR(A‚B) / [(σA)(σB)] = -0.0322 / (14%)(23%) rA‚B = -1 But when rA‚B = -1
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PDF and CDF) Two random variables X and Y have joint pdf: fX‚Y (x‚ y) = csin(x + y) 0 ≤ x ≤ π/2‚ 0 ≤ y ≤ π/2 (a) Find the value of the constant c. (b) Find the joint cdf of X and Y . (c) Find the marginal pdf’s of X and of Y . (d) Find the mean‚ variance‚ and covariance of X and Y . 4. (Uncorrelated vs. Independent) (a) We have seen that independence of two random variables X and Y implies that they are uncorrelated‚ but that the converse is not true. To see this‚ let Θ be uniformly distributed
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