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The answer of the question “Who carried out the survey?”
Answer to Problem 1CS
Solution: The required answer is “The Pew Research Center.”
Explanation of Solution
The provided study is done by “The Pew Research Center.” So, the answer for the question “Who carried out the survey?” will be “The Pew Research Center.”
The answer of the question “What was the population?”
Answer to Problem 1CS
Solution: The required answer is all American adults with residential telephone.
Explanation of Solution
The population can be defined as a set of all individuals who are eligible as subjects for a particular study. In the provided study, all the American adults who have residential telephone are eligible for the study because the research question is asked to the Americans adults. Therefore, the answer that is given by “The Pew Research Center” for the question “What was the population?” will be all American adults with residential telephone.
The answer of the question “How was the sample selected?”
Answer to Problem 1CS
Solution: The required answer will be the sample is who completes the survey among 2879 residents.
Explanation of Solution
In the provided study, the sample was collected after calling 2879 residents. Therefore, the required answer that is given by “The Pew Research Center” will be the resident who completes the survey is considered as the sample.
The answer of the question “How large was the sample?”
Answer to Problem 1CS
Solution: The required answer is 1000 residents.
Explanation of Solution
In the provided study, the research question is asked to 1000 residents. So, the required answer will be 1000 residents.
The answer of the question “What was the response rate?”
Answer to Problem 1CS
Solution: The required answer will be that the response rate is 42%.
Explanation of Solution
The response rate for any study can be obtained if the number of respondents who answer the research question is known. In the provided study, the nonresponse rate is 58%. So, the response rate is calculated as
The answer of the question “How were the subjects contacted?”
Answer to Problem 1CS
Solution: The required answer is that the subjects are contacted through telephone.
Explanation of Solution
In the provided study, the subjects of the study are contacted through the telephone interview. Therefore, the required answer for the particular question would be that the subjects are contacted through telephone.
The answer of the question “What were the exact questions asked?”
Answer to Problem 1CS
Solution: It is not possible to answer the provided question.
Explanation of Solution
As the exact question asked to the respondents is not provided, the question “What were the exact questions asked?” is not possible to answer.
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Chapter 4 Solutions
Statistics: Concepts and Controversies
- 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?arrow_forwardV2 360 Step down + I₁ = I2 10KVA 120V 10KVA 1₂ = 360-120 or 2nd Ratio's V₂ m 120 Ratio= 360 √2 H I2 I, + I2 120arrow_forwardQ2. [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).arrow_forward
- 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
- The scores of 8 students on the midterm exam and final exam were as follows. Student Midterm Final Anderson 98 89 Bailey 88 74 Cruz 87 97 DeSana 85 79 Erickson 85 94 Francis 83 71 Gray 74 98 Harris 70 91 Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary. Test statistic: rs =arrow_forwardBusiness discussarrow_forwardBusiness discussarrow_forward
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