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- I need the answer as soon as possible(a) Let X defines the length in meter. The probability density function of X is f(x) = x + 1 where a < x < 2 meter. Find a.(1 point) Which of the following is/are always true about a continuous random variable? CHECK ALL THAT APPLY. VA. The probability that it has a value equal to x is given by f(x) where f is the density function. VB. The probability that it has a value that falls between real values a and b is given by the area under the density function over the range (a, b). OC. It can only take on integer values. OD. None of the above
- Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x) = k(2 - x), 0The probability density curve of a random variable X is given in the following figure. The possible values for X range from 20 to 50.Verify that the function corresponding to the figure to the right is a valid probability density function. Then find the following probabilities: a. P(x 8) c. P(7 0 for all values of x and the total area under the density function above the x-axis is O D. (Type an integer or a decimal. Do not round.) the given function is a valid probability density function.Since height is a continuous numerical variable, its probability density function is represented by the smooth curve below. What is true about the area under the curve? 140 160 180 200 height (cm) The area does not represent all possible heights, so the area under the curve and probability are both 0. O The area does not represent all possible heights, so the area above the curve is 1. O The area represents all possibile heights, so the area and probability are both 100. The area represents all possible heights, so the area under the curve and probability of all the height occurring are both 1.Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 0.6 1 0.01 2 0.14 x P(X=x) 0 310 1 110 2 25 x P(X=x) 0 18 1 14 2 58 x P(X=x) 0 0.13 1 0.09 2 0.45 3 0.27 4 0.06 x P(X=x) 0 −15 1 310 2 12 3 310 4 110 x P(X=x) 0 12 1 18 2 38A manufacturing company has developed a machine for cleaning carpet that is fuel-efficient because it delivers carpet cleaner so rapidly. Of interest is a random variable Y, the amount in gallons per minute delivered. It is known that the density function is given to the right. Complete parts (a) and (b) below. 2sys6, f(y) 0, elsewhere (a) Sketch the density function. Choose the correct graph below. O A. В. C. D. f(y) 1.2- Af(y) 1.2- Af(y) 1.2- Q Af(y) 12- 0.9- 0.6- 0.9- 0.6- 0.9 9- 0.6- 6- 0.3- 0.3- 0.3- 3- y y y y 0 0 3 0+ 3 04 0.4 0.8 1.2 0+ 6 9 12 6. 12 9 12 (b) Give E(Y), E(Y), and Var(Y). E(Y) = (Simplify your answer.)The following density function describes a random variable X. f(x) = 1 – ; if 0At a restaurant, the density function for the time a customer has to wait before being seated is given by f(t) = 2e¯ if t > 0. Find the probability that a customer will have to wait at least 6 minutes for a table. Probability = .000006 -2tThe table below shows an incomplete probability density function for X , the number of imperfections per batch of jeans that just came off a production line. What should the missing probability be? Provide the final answer as a decimal. x P(X = x) 0 0.88 1 0 2SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman