Problem 4. In Section 3.2-4 it was shown that the minimum frequency separation for orthogonality of binary FSK signals with coherent detection is Af = 1/2T. However, a lower error probability is possible with coherent detection of FSK if Af is increased beyond 1/2T. Show that the optimum value of Af is 0.715/T, and determine the probability of error for this value of Af.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Problem 2-5.5. But change the problem to say Gaussian noise variance of 2, and threshold of 6V.Problem#1: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for(a) 1 hour(b) 15 minutes(c) 8 hours
- Problem 1 One of the advantages that concrete structures have over steel structures is fire resistance (which is to say, steel becomes weak when heated). The time, T, that it takes a steel girder to reach certain temperature (where its strength becomes too low to support its load) in a fire is, however, random. Suppose that for design code development, the following data have been gathered on the time T in hours: 0.736, 0.863, 0.865, 0.913, 0.915, 0.937, 0.983, 1.007, 1.011, 1.064, 1.109, 1.132, 1.140, 1.153, 1.253, 1.394 (a) Compute the values of the sample mean and the sample median by hand. (b) By how much could the smallest sample observation be increased without affecting the value of the sample median? (c) By how much could the smallest sample observation be increased without affecting the value of the sample mean? (d) Compute the values of the first quartile, third quartile, interquartile range, lower fenceQuestion 4a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:• the type of distribution this variable has; and• the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error.iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%. iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the…QUESTION 5 The decision rule for a Wilcoxon signed-rank test is always to reject H0 if W is greater than or equal to the critical value. True False
- Question 1The following table shows the number of shirts by sizes that are manufactured in a factory on aparticular week:Extra Small Small Medium Large Extra Large 390 470 520 680 440a) It was discovered that the sizing of some shirts was labelled incorrectly.(i) Give two reasons why it would be necessary to examine a sample of the shirts producedrather than examine the entire weekly production.(ii) State two differences between a cluster sample and a stratified random sample in thissituation. (iii) Using the stratified random sampling technique, calculate the number of medium shirtsthat will be selected if we require a sample of 375 shirts.Section 9.3 Question #2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d-- and sd. In general, what does μd represent? Temperature (°F) at 8 AM 98.2 99.1 97.2 97.7 97.5 Temperature (°F) at 12 AM 99.0 99.8 97.5 97.3 97.9 Let the temperature at 8 AM be the first sample, and the temperature at 12 AM be the second sample. Find the values of d-- and sd. _ d= _________________ (Type an integer or a decimal. Do not round.) sd= ____________ (Round to two decimal places as needed.) In general, what does μd represent? A. The difference of the population means of the two populations B. The mean of the differences from the population of matched data C. The mean value of the differences for the paired sample data D. The mean of the means of each matched pair from the population of matched…Question 23: The National Institute of Mental Health published an article stating that in any one-year period, approximately 9% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 10% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 9% in the general adult American population. Test the relevant hypotheses using a 10% level of significance. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: Based on the hypotheses, find the following: Test Statistic = p-value = Based on the above we choose to The correct summary would be: that the true proportion of people in that city suffering from depression or a…
- Problem 1: A report states that on average Moroccan boys (12-18 years old) get a haircut 5.8 times a year. An independent researcher randomly selected 20 boys (12-18 years old) and obtained these data. 3 2 1 3 7 2 9 4 6 6 8 0 5 6 4 2 1 3 4 1 At α = 0.05, can it be concluded that the average is more than 5.8 visits per year? (Hint: use the t test)Question 15 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 human errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.Question 13 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 technical errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.
