Business Statistics: A First Course (7th Edition)
7th Edition
ISBN: 9780321979018
Author: David M. Levine, Kathryn A. Szabat, David F. Stephan
Publisher: PEARSON
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Chapter 1, Problem 1.35CYU
To determine
To explain: The difference between
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For a binary asymmetric channel with Py|X(0|1) = 0.1 and Py|X(1|0) = 0.2; PX(0) = 0.4 isthe probability of a bit of “0” being transmitted. X is the transmitted digit, and Y is the received digit.a. Find the values of Py(0) and Py(1).b. What is the probability that only 0s will be received for a sequence of 10 digits transmitted?c. What is the probability that 8 1s and 2 0s will be received for the same sequence of 10 digits?d. What is the probability that at least 5 0s will be received for the same sequence of 10 digits?
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120
Q2. [20 points] An amplitude X of a Gaussian signal x(t) has a mean value of 2 and an RMS value of
√(10), i.e. square root of 10. Determine the PDF of x(t).
Chapter 1 Solutions
Business Statistics: A First Course (7th Edition)
Ch. 1 - Four different beverages are sold at a fast-food...Ch. 1 - U.S. businesses are listed by size: small, medium,...Ch. 1 - Prob. 1.3LBCh. 1 - Prob. 1.4ACCh. 1 - Prob. 1.5ACCh. 1 - Prob. 1.6ACCh. 1 - For each of the following variables, determine...Ch. 1 - Prob. 1.8ACCh. 1 - Prob. 1.9ACCh. 1 - Prob. 1.10AC
Ch. 1 - The director of market research at a large...Ch. 1 - Prob. 1.12ACCh. 1 - Prob. 1.15ACCh. 1 - Prob. 1.17LBCh. 1 - Fora population of N = 902, verify that by...Ch. 1 - Given a population of N = 93, starting in row 29,...Ch. 1 - Prob. 1.20ACCh. 1 - You want to select a random sample of n = 1 from a...Ch. 1 - Prob. 1.22ACCh. 1 - The registrar of a university with a population of...Ch. 1 - Prenumbered sales invoices are kept in a sales...Ch. 1 - Prob. 1.26ACCh. 1 - Prob. 1.27ACCh. 1 - Prob. 1.30ACCh. 1 - Prob. 1.31CYUCh. 1 - Prob. 1.32CYUCh. 1 - Prob. 1.33CYUCh. 1 - Prob. 1.34CYUCh. 1 - Prob. 1.35CYUCh. 1 - Results of a 2013 Adobe Systems study on retail...Ch. 1 - Prob. 1.38CRPCh. 1 - Prob. 1.39CRPCh. 1 - Prob. 1.40CRPCh. 1 - Prob. 1.42CRPCh. 1 - A manufacturer of cat food is planning to survey...
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- In a network with 12 links, one of the links has failed. The failed link is randomlylocated. An electrical engineer tests the links one by one until the failed link is found.a. What is the probability that the engineer will find the failed link in the first test?b. What is the probability that the engineer will find the failed link in five tests?Note: You should assume that for Part b, the five tests are done consecutively.arrow_forwardProblem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…arrow_forwardProblem 1. Multi-stock model We consider a 2-stock model similar to the one studied in class. Namely, we consider = S(1) S(2) = S(¹) exp (σ1B(1) + (M1 - 0/1 ) S(²) exp (02B(2) + (H₂- M2 where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with t≥0 Cov (B(¹), B(2)) = p min{t, s}. " The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian motion (W+)+20 (W(1), W(2))+20 such that = S(1) S(2) = = S(¹) exp (011W(¹) + (μ₁ - 01/1) t) 롱) S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t). where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p). Hint: The constants will follow the formulas developed in the lectures. (a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2) functions of (B(1), B(²)). as (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…arrow_forward
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- I just need to know why this is wrong below: What is the test statistic W? W=5 (incorrect) and What is the p-value of this test? (p-value < 0.001-- incorrect) Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages pages 127 217 486 132 397 297 396 327 292 256 358 272 What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12 Alpha Level 0.001 0.005 0.01 0.025 0.05 0.1 0.2 Critical Value 75 70 68 64 60 56 50 What is the p-value for this test? p-value < 0.001arrow_forwardons 12. A sociologist hypothesizes that the crime rate is higher in areas with higher poverty rate and lower median income. She col- lects data on the crime rate (crimes per 100,000 residents), the poverty rate (in %), and the median income (in $1,000s) from 41 New England cities. A portion of the regression results is shown in the following table. Standard Coefficients error t stat p-value Intercept -301.62 549.71 -0.55 0.5864 Poverty 53.16 14.22 3.74 0.0006 Income 4.95 8.26 0.60 0.5526 a. b. Are the signs as expected on the slope coefficients? Predict the crime rate in an area with a poverty rate of 20% and a median income of $50,000. 3. Using data from 50 workarrow_forward2. The owner of several used-car dealerships believes that the selling price of a used car can best be predicted using the car's age. He uses data on the recent selling price (in $) and age of 20 used sedans to estimate Price = Po + B₁Age + ε. A portion of the regression results is shown in the accompanying table. Standard Coefficients Intercept 21187.94 Error 733.42 t Stat p-value 28.89 1.56E-16 Age -1208.25 128.95 -9.37 2.41E-08 a. What is the estimate for B₁? Interpret this value. b. What is the sample regression equation? C. Predict the selling price of a 5-year-old sedan.arrow_forward
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