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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and (C) The range of the data that would contain 68% of the results. (5 points). Raw data: sales/month (Millions of $) 23 45 34 34 56 67 54 34 45 56 23 19 Descriptive Statistics: Sales | Variable | Total Count | Mean | StDev | Variance | Minimum | Maximum | Range | Sales | 12 | 40.83 | 15.39 | 236.88 | 19.00 | 67.00 | 48.00 | Stem-and-Leaf Display: Sales Stem-and-leaf of Sales N = 12 Leaf Unit = 1.0 | 1 | 1 | 9 | 3 | 2 | 33 | 3 | 2 | | 6 |
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CONFIDENTIAL CS/JAN 2012/QMT500 UNIVERSITI TEKNOLOGI MARA FINAL EXAMINATION COURSE COURSE CODE EXAMINATION TIME STATISTICS FOR ENGINEERING QMT500 JANUARY 2012 3 HOURS INSTRUCTIONS TO CANDIDATES 1. This question paper consists of five (5) questions. 2. Answer ALL questions in the Answer Booklet. Start each answer on a new page. Do not bring any material into the examination room unless permission is given by the invigilator. Please check to make sure that this examination pack
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Mean and Variance of the Binomial Distribution The probability distribution of the Bernoulli trial with random variable X is given by Table 1 X=x P(X=x) 0 1-p 1 p The expectation and variance can be calculated as follow E X 01 p 1 p p Mean and Variance of the Binomial Distribution The expectation and variance can be calculated as follow Var X 0 1 p 1 p p 2 2 p p2 p1 p pq 2 Mean and Variance of the Binomial
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Lecture Notes in Financial Econometrics (MSc course) Paul Söderlind1 1 January 2013 of St. Gallen. Address: s/bf-HSG‚ Rosenbergstrasse 52‚ CH-9000 St. Gallen‚ Switzerland. E-mail: Paul.Soderlind@unisg.ch. Document name: FinEcmtAll.TeX 1 University Contents 1 Review of Statistics 1.1 Random Variables and Distributions . . . . . . . . . . . . . . 1.2 Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Distributions Commonly Used in Tests . . . . . . . . . . . . . 1
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a.The mean return should be less than the value computed in the spreadsheet. The fund’s return is 5% lower in a recession‚ but only 3% higher in a boom. The variance of returns should be greater than the value in the spreadsheet‚ reflecting the greater dispersion of outcomes in the three scenarios. b.Calculation of mean return and variance for the stock fund: (A) (B) (C) (D) (E) (F) (G) Scenario Probability Rate of Return Col. B Col. C Deviation from Expected Return Squared Deviation Col. B
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Observation = estimated relationship + residual: yi =+ ei => yi = b1 + b2 x + ei Assumptions underlying model: 1. Linear Model ui = yi - 1- 2xi 2. Error terms have mean = 0 E(ui|x)=0 => E(y|x) = 1 + 2xi 3. Error terms have constant variance (independent of x) Var(ui|x) = 2=Var(yi|x) (homoscedastic errors) 4. Cov(ui‚ uj )= Cov(yi‚ yj )= 0. (no autocorrelation) 5. X is not a constant and is fixed in repeated samples. Additional assumption: 6. ui~N(0‚ 2) => yi~N(1- 2xi‚ 2)
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Part 1 of 1 - | Question 1 of 10 | 1.0 Points | Consider the following scenario in answering questions 1 through 4. Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance. State the null and alternative
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of paper. Please highlight your answers so we can find them easily. 1. Compute and report the mean returns‚ variances‚ and standard deviations for the two stocks. In addition‚ compute the covariance and the correlation between the two stock returns. Report all numbers as annualized. (Hint: annualized variance is equal to 12*monthly variance. Also‚ please do not report variances and covariances in %‚ which would not make sense.) 2. Plot the mean-standard deviation graph for a portfolio
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been reviewing random variables. RVs have certain properties such as mean that measures the center‚ and variance that measures the dispersion. We would like to make claims about these properties and test them using statistical methods. Over the past years‚ Wall Street has been very interested in the volatility of the stocks. In this case‚ we would want to make sound claims about variances. We start with a null hypothesis Ho‚ which is the claim that we will test. It looks as such: In this
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