"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period o heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. x! f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. F(x) = x< 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to three decimal places.) 016 Use the cdf from (b) to determine the probability that headway is between 2 and sec. (Round your answer to three decimal places.) .014 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your answers to three decimal places.) mean .6 standard deviation (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

Utility is a type of function that occurs in economics. When a consumer receives x units of a certain​ product, a certain amount of​ pleasure, or utility​ U, is derived. The graph represents a typical utility function.

As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): X 1= average high school grade in mathematics (HSM) X 2 = average high school grade in science (HSS) X 3 = average high school grade in English (HSE) X 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to the data with the following results: SOURCE DF MS F VALUE PROB>F MODEL 28.64 5.73 11.69 0001 ERROR 218 106 82 0.49 TOTAL 223 135.46 ROOT MSE DEP MEAN 0.700 R-SQUARE 0.211 4.635 ADJ R-SQ 0.193 PARAMETER STANDARD T FOR O VARIABLE ESTIMATE ERROR PARAMETER -0 PROB> ITI INTERCEPT 2.327 0.039 5.817 0.0001 0.0003 XI HSM) X2 (HSS) X3 (HSE) X4 (SATM) X5 (SATV) 0.146 0.037 3.718 a.036 0.038 0.950 0.3432…

drivers of that Age - ]]], [16 – 17,1,55], [18 - 19,2,30], [20 - 24, 3, A traffic safety organization has compiled data in an urban region of Canada on the rate of non-fatal vehicle injury accidents, y, as a function of the age of the driver, x. The data is shown below. It is assumed that an injury accident affects either the driver or passengers or others external to the vehicle and does not result in death. Age Range of x, Designated Age Driver Category of Driver y, Number of Injury Accidents per 10 million km driven by drivers of that Age 16-17 1 55 18-19 2 30 20-24 3 24 25-29 4 22 30-39 5 14 40-49 6 13 50-59 7 12 60-69 8 10 70-79 9 14 10