c. X is a zero mean Gaussian random variable with variance σ 2 . 4.100 Let X be the number of successes in n Bernoulli trials where the probability of success is p. Let Y = X/n be the average number of successes per trial. Apply the Chebyshev inequality to the event {|Y − p| > a}. What happens as n → ∞? 4.102 a. Find the characteristic function of the random variable X uniformly distributed over [−b‚ b). b. Find the mean and variance of X by applying the moment theorem. 4.105 modified
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probability (7%) 1. Let the random variable X follow a Binomial distribution with parameters n and p. We write X ~ B(n‚p). * Write down all basic assumptions of Binomial distribution. * Knowing the p.m.f. of X‚ show that the mean and variance of X are = np‚ and 2 = np(1 – p)‚ respectively. 2. A batch contains 40 bacteria cells and 12 of them are not capable of cellular replication. Suppose you examine 3 bacteria cells selected at random without replacement. What is the probability
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Normal Distribution Normal distribution is a statistics‚ which have been widely applied of all mathematical concepts‚ among large number of statisticians. Abraham de Moivre‚ an 18th century statistician and consultant to gamblers‚ noticed that as the number of events (N) increased‚ the distribution approached‚ forming a very smooth curve. He insisted that a new discovery of a mathematical expression for this curve could lead to an easier way to find solutions to
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distribution of predictions for the population of financial analysts is normal. a) The probability is 0.10 that the sample variance is more than what percentage of the population variance? b) Determine any pair of numbers a and b to complete the following sentence: The probability is 0.95 that the sample variance is between a% and b% of the population variance. 2. A random sample of 202 vice presidents of marketing in corporations from the manufacturing sector were given a list
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information. We define σt to be the time t 2 conditional variance of ηt+1 or the conditional expectation of ηt+1 . We assume the conditional on time t information‚ the innovation is normally distributed: 2 ηt+1 ∼ N (0‚ σt ) (1) The unconditional variance of the innovation‚ σ 2 ‚ is just the unconditional 2 expectation of σt . 2 2 σ 2 ≡ E[ηt+1 ] = E[σt ] (2) 2 The variability of σt around its mean does not change the unconditional 2 2 variance σ . The variability of σt does affect higher moments
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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)‚ we can estimate
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Running Heading: COST ALLOCATION AND VARIANCES Cost Allocation and Variances- Chapter 12 & 13 Text Book Questions Stacey S. Swafford University of Phoenix ACC 561 Dr. Janice Mereba April 23‚ 2010 Chapter 12 Excel Application Exercise 12-59: Allocating Costs Using Direct and Step-Down Methods p. 584 Goal: Create an Excel spreadsheet to allocate costs using the direct method and the step-down method. Use the results to answer questions about your findings. Scenario: Antonio
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http://www.nbcc.org/NCE/Sample n attempting to understand the life perspectives and characteristics of their clients‚ some counselors use Kohlberg’s theory of moral development as a theoretical framework. These counselors know that Kohlberg’s theory includes three progressive levels culminating in: principled thought‚ wherein the individual adopts a self-accepted set of standards of behavior personhood‚ wherein the individual is free from moral dilemmas self-actualization‚ wherein the individual
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this tool to compute the global minimum variance portfolio and the tangency portfolio for the three-firm example (see the spreadsheet 3firm.xls). The spreadsheet for this tutorial is called solverex.xls. The data for this example are given in the following table Stock 1 2 3 E[R] 0.229 0.138 0.052 VAR(R) 0.924 0.862 0.528 COV(I‚J) 0.063 -0.582 -0.359 PAIR(I‚J) (1‚2) (1‚3) (2‚3) For convenience‚ I have named the cells containing the expected returns‚ variances and covariances. See the 483solverex
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NAME: ANSWER KEY Econometrics First Test‚ Queens College‚ I. R. Kelly Thursday‚ September 27th‚ 2012‚ 9:25-10:40am Please put all answers on the question sheet. You have one hour and fifteen minutes to finish the test. Best of luck. 1. (6 points) How does a panel data set differ from a regular pooled data set? Give a specific example. A pooled data set is one that combines both time series and cross-sectional data; in other words‚ there are many cross-sectional units over a period of time
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