The population (p) of a small community on the outskirts of a city grows rapidly over a 20- year period: t (time) p (population) 10 15 20 100 200 450 950 2000 As an engineer working for a utility company, you must forecast the population 5 years into the future in order to anticipate the demand for power. Use an exponential model and linear regression to make this prediction. Determine r?. Plot the data along with the curve.
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- variables c.d 00 01 11 10 Answer: 00 Karnaugh table q = f(a, b, c, d) variables a, b 01 11 1 1 e 10 A function of how many variables is represented by the rectangle surrounding 1s (and no more) showed in the Karnaugh table? -1 if there is no such function.1. The impulse response of a causal system is: h(t) = A cos(wt) e¯¹/¹u(t) where u(t) is the Heaviside step function. The response is measured experimentally with a sampling interval of T. a. Write an expression for the sampled impulse response h[n]. b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tables provided below as necessary. c. Does the system have an infinite impulse response (IIR) or finite impulse response (FIR)? Justify your answer. d. What is the DC gain of H[z]? e. Write a difference equation that describes the output y[n] in terms of input x[n].Solve in R programming language: 5) Use R to calculate and simulate with the exponential distribution as follows. (a) For an exponential random variable X with λ = 4, simulate 1000 independent exponential random variables by using the R function rexp(n, λ). Calculate the mean and variance of this sample. (b) Compare the empirical results from part (a) with the distribution mean 1/λ and the distribution standard deviation 1/λ.
- 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.A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 6 of the calls involve a fax message?(b) What is the probability that exactly 6 of the calls involve a fax message?(c) What is the probability that at least 6 of the calls involve a fax message?(d) What is the probability that more than 6 of the calls involve a fax message?Suppose the U.S. Census Bureau projects the population of the state to be 2.6 million in 2003 and 4.1 million in 2023. Assuming the population growth is linear, Use t years since 1993 and p the population of the state in millions. According to your linear model, what is the population of the state in 2032? (Round your final answer to two decimal places}.
- We want to predict maintenance expense ( y) for a truck during the current year, from the independent variables x1 miles driven (in thousands) during the current year and x2age of the truck (in years) at the beginning of the current year. We are given the information inGiven the following values (200, 400, 800, 1000, 2000): Calculate their mean, variance, and standard deviation. Normalize them using min-max normalization with and . Normalize them using z-score.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).
- Use Matlab to solve the threshold population equation : P(t)= -rP(1-P/K)(1-P/T) , P(0)=13050. Where r=0.042, K=7,000 and T=5,000.You have built a classification model to predict if a patient will be readmitted within 30 days of discharge from the hospital. When you examine the ROC curve you find that it essentially coincides with the central diagonal of the curve. Based on this, which of the following can you infer: Your model performs about as good as random guessing Your model performs much worse than random guessing Your model performs much better than random guessingConsider 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 % %