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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.Explain the difference between the average rate of change of y as x changes a to b, and the instantaneous rate of change of y at x=a
- asysb, If the density function of Y is f(y)={ b-a' 0, Otherwise. then the variance of Y is equal to Select one: (b-a) a. 12 (a+b? Ob. 12 a+b2.5 Y has a density function S0) = (2 y), 0 < y < 2 elsewhere Find the mean and variance of Y.Y has a density function + y, Osys1, Ry) = {7 0, elsewhere. Find the mean and variance of Y. (Round your answers to four decimal places.) E(Y) = V(Y) =
- 4. What are the median, and mode, respectively, for the density function f(x) = Ta (1 + x²)'Normal distribution. The moment generating function of a random variable U is M(t) = (1 - 8t)^-7. Find: i)Probability density function, ii)Mean, iii)Variance of U.Q. 6 The percentage of impurities per batch in a chemical product is a random variable X with density function fx(x)=12x² (1–x); 0Ук. Suppose that Y₁. Y₂; Yn 15. 2 from Function random Sample a population with probability density f(y) = find the maximum BY 1-B B like hood ozy 21: B >0 Elsewhere Estimator of BSk(x + 4y) ,0 < x < 2, 0 < y < 1 Let f(x,y) = {K** ,otherwise be the joint probability density of X and Y. iv. Find the correlation coefficient of X and Y. V. Find the variance of Z = 6X + 8Y + 10.Find the marginal PDFs of X and Y.SEE MORE QUESTIONS
