3.1 The proportion of time per day that all checkout counters in a Checkers Hypermarket are busy is a random variable Y with a density function given by (10y²(1 – y), 0, 0 < y < 1 elsewhere f(v) = Find the mean and standard deviation and interpret your answer.
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- Please answer with a proper explanation.Let X have beta distribution with a =2 and B = 3. Then the mean and the variance of X, respectively, are Select one: O a. 0.04 and 04 O b. 0.02 and 0.04 O c. 0.4 and 0.04 O d. 0.4 and 0.20 The weekly downtime Y (in hours) for a certain industrial machine has approximately gamma distribution a =3 and B =2. The loss, in dollars, to the industrial operation as a result of this downtime is given by L = 30Y+2Y?. Find the expected value of L. Select one: O a. 180 O b. 98 Oc. 36 O d. 276 The length X to complete a certain key task in house construction is exponentially distributed with mean of 5 hours. The cost of completing this task is C = 10+20x2, Find the expected cost. Select one: O a. 1000 O b. 1010 O c. 510 O d. 500 sum of the dead load plus the The total sustained load on the concrete footing of a planned building is occupancy load. Suppose that the dead load X, has a gamma distribution with a = 10 and B= 30, whereas the occupancy load, X2 also has exponential distribution with e =…Y has a distribution function (0, ys0, 24 F(y) = 09. Zero-mean Gaussian random variables x and y have variance oz= 3 and o= 4 respectively and a y -1 correlation coefficient p = ing Write an expression for the joint density function.Suppose X is a random variable defined as final cost of project estimated cost of project which has a PDF as follows: [0 xa a. Determine the value of a. b. What is the probability that the final cost of a project will exceed its estimated cost by 25%? c. Determine the mean value and standard deviation of X.1.4 The pH of milk samples from Dairy Belle is a random variable Y with probability density function given by ((1/9)(4 – y)?,5Find the value of k which make the following function a pdf (15 y - 2 sys0 64' 64 fW) ={ 3 + ky 0 < y< 3 8 elsewhere What is the P(-1 < Y S 2)? Find the cumulative distribution function of Y. Find the variance of Y.DHL usually gives its customer a 60-minute window in which it expects home deliveries to be delivered. An independent consultant estimates that the final delivery time within the window is a delivery that follows the following condensation function:a. Draw the density function of the event. b. What is the expected value of the transaction? c. What is the variance of the event?1. The density function for random variable X is f(x). Find variance for the random variable X. Leave your answers as reduced fractions. f(x) = {16 x+0Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.2.4 Solve the below problem: The change in depth of a river from one day to the next, measured (in feet) at a specific location, is a random variable Y with the following density function: - 3 < y< 3, f(y) = (0, elsewhere. 2.4.1. What type of distribution does Y follow? 2.4.2. Find E (Y) (Hint: Use the distribution function).Ук. 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 BSEE 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