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- An assignment was given to four students attending a sample survey course. The problem was to estimate the average time per week devoted to study in Punjab Agricultural University (PAU) library by the students of this university. The university is running undergraduate, master's degree and doctoral programs. Number of students registered for the three programs is 1300, 450, and 250 respectively. Since the value of the study variable is likely to differ considerably with the program, the investigator divided the population of students into 3 strata: undergraduate program (stratum I), master's program (stratum II), ånd doctoral program (stratum III). First of the four students selected WOR simple random samples of sizes 20, 10, and 12 students from strata I, II, and III respectively, so that, the total sample is of size 42. The information about weekly time devoted in library is given in table 5.1. Table 5.1 Time (in hours) devoted to study in the university library during a week Stratum…Question: Suppose there are n people in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals. The gossip problem asks for G(n), the minimum number of telephone calls that are needed for all n people to learn about all the scandals. a). Find G(1), G(2), G(3), and G(4). b). Use mathematical induction to prove that G(n) 4. [Hint: In the inductive step, have a new person call a particular person at the start and at the end.] c). Prove that G(n)= 2n – 4 for n> 4.Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 P(t) = (a) Census data for the United States between 1790 and 1950 are given in the table above. Construct a logistic population model using the data from 1790, 1860, and 1920. (Assume that t is years since 1790 and P is population in millions. Round all coefficients to four decimal places.) 143.56 1+ 35.53e Year Population (in millions) 3.929 5.308 7.240 9.638 12.866 17.069 23.192 31.433 38.558 50.156 62.948 75.996 91.972 1820 (b) Construct a table comparing actual census population with the population predicted by the model in part (a). Compute the error and the percentage error for each entry pair. 1910 -0.0353-t) 105.711 122.775 131.669 150.697 Census Population (in Millions) 9.638 91.972 Predicted Population (in Millions, rounded to three decimal places) 9.989 9.174 X Error (rounded to three decimal places) -0.351 0 % Error (rounded to two decimal places) -3.64 0 % %
- You are an investor who receives daily price quotes for a stock. The span of a stock's price on a given day is the number of consecutive days, from the given day going backwards, on which its price was less than or equal to its price on the day we are considering. Thus, the Stock Span Problem is as follows: Given a series of daily price quotes for a stock, find the span of the stock on each day of the series. Assume you are given seven daily stock quotes: 3, 10, 4, 7, 9, 6, and 8. Assume further that these stock quotes are stored in the array quotes. Show a step-by-step, manual desk-check execution of the algorithm below showing the values of all variables and arrays for each step in each cycle of each loop, as demonstrated in clase Algorithm: A Simple Stock Span Algorithm SimpleStockSpan (quotes) spans Input: quotes, an array with n stock price quotes Output: spans, an array with n stock price spans 1 spans CreateArray (n) 2 for i-0 to n do k+1 span_endFALSE while i-k 20 and not…You are an investor who receives daily price quotes for a stock. The span of a stock's price on a given day is the number of consecutive days, from the given day going backwards, on which its price was less than or equal to its price on the day we are considering. Thus, the Stock Span Problem is as follows: Given a series of daily price quotes for a stock, find the span of the stock on each day of the series. Assume you are given seven daily stock quotes: 3, 10, 4, 7, 9, 6, and 8. Assume further that these stock quotes are stored in the array quotes. Show a step-by-step, manual desk-check execution of the algorithm below showing the values of all variables and arrays for each step in each cycle of each loop, as demonstrated in clase Algorithm: A Simple Stock Span Algorithm SimpleStockSpan (quotes) → spans Input: quotes, an array with n stock price quotes Output: spans, an array with n stock price spans 2 3 4 5 6 7 8 10 11 spans CreateArray (n) ← for i0 to n do k 1 span_end FALSE while…Customers are used to evaluate preliminary product designs. In the past, 91% of highly successful products received good reviews, 57% of moderately successful products received good reviews, and 15% of poor products received good reviews. In addition, 40% of products have been highty successful, 35% have been moderately successful and 25% have been poor products. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that a product attains a good review? (b) If a new design attains a good review, what is the probability that it will be a highly successful product? (c) If a product does not attain a good review, what is the probability that it will be a highly successful product? (a) 5985 (b) 6082 (c) i 0897
- The table below describes the average voltage generated, A, in volts by an energy harvester for three days at three different times for each day. Referenced time Day 3. 3.0 V 1.8 V 0.9 V 1.9 V 2.2 V 1.7 V 0.5 V 1.1 V 2.2 V Given that the power generated in millivwatts (mW), P, can be calculated using the following equation: 500A? P = Where A is the voltage generated and R is the total resistance given as 2000 Q. Write a MATLAB/OCTAVE script to store the voltage data from the table as a single matrix, where the days represent the rows and the referenced times represent the columns of the matrix. Hence, in the same script, Calculate the power generated at each day and referenced time. i) ii) Compute and output the overall maximum power generated. Finally, compute and output the days and referenced times where the power generated exceeds 1.0 mW (Tips: You may want to use a nested loop OR the in-built MATLAB/OCTAVE function called 'find' here) iii)Solve in R programming language: Suppose that the number of years that a used car will run before a major breakdown is exponentially distributed with an average of 0.25 major breakdowns per year. (a) If you buy a used car today, what is the probability that it will not have experienced a major breakdown after 4 years. (b) How long must a used car run before a major breakdown if it is in the top 25% of used cars with respect to breakdown time.Homework İTÜ A laboratory test was performed to obtain the change of concentration with time. Test results are shown on the table. The student Concentration Time (s) (mg/L) noticed that one datum at t=20s is missing. 194 - Use interp1() function to predict the missing value using different methods: 10 246 15 369 >linear 25 384 > cubic > spline 30 271 40 24 - Plot the results on the same figure. ISTANBUL TEKNİK ÜNİVERSİTESİ Artentr ougt 2020-21 Spring Homework #3 -– Tolga Y. Ozudogru, Ph.D.
- Students graduating Atlantis University are being administered a test to check their general competence level at the end of the study program. From a random sample of 100 students, 95 passed and 5 failed. We aim to construct a 95% confidence interval for the proportion p of students at Atlantis University who have achieved a satisfactory competence level after their studies. Answer the following questions: (a) The critical z-value for this problem (the z-value to be used) is z = (give the exact value to TWO decimal places N.xx) (b)The middle of the interval is %. (ROUND to the nearest integer) (c) The error margin is % (use one decimal only and give in terms of percentages).Information on morphine: Morphine can be administered via injection / IV. The quantity of morphine in a given dose may vary, but one guideline is to use 0.1 mg of morphine for each kg of the patient's body mass. The time taken for half the quantity of morphine to be removed from the body is 2 hours. An exponential function can be used to model the amount of morphine in the body over time: ?=?0???A=A0ekt (note that ?k will be negative). Calculate the value of ?k for morphine. Write a Python function called MorphineModel, which takes two arguments: dose amount ?0A0 and time since last dose ?t, and returns the amount of morphine in the body at this time ?t. Add to your computer code so that you have a program which is an implementation of the following flowchart. Ensure that your code is well-communicated to a user of the program (via the print statements) and well-communicated to someone reading the code (via comments).3 Lindon Company is the exclusive distributor for an automotive product that sells for $22.00 per unit and has a CM ratio of 30%. The company's fixed expenses are $105,600 per year. The company plans to sell 17,400 units this year. Required: 1. What are the variable expenses per unit? (Round your "per unit" answer to 2 decimal places.) 2. What is the break-even point in unit sales and in dollar sales? 3. What amount of unit sales and dollar sales is required to attain a target profit of $39,600 per year? 4. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $2.20o per unit. What is the company's new break-even point in unit sales and in dollar sales? What dollar sales is required to attain a target profit of $39,600? 4 points 1. Variable expense per unit 2. Break-even point in units Break-even point in dollar sales 3. Unit sales needed to attain target profit Dollar sales needed to attain target profit 4. New break-even point in unit…