Suppose X, Y have joint density function ƒ (x, y) = { # (xy + y²), 0≤x≤1 and 0≤y≤1 1 0, f otherwise. (a) Check that fis a genuine joint density function. (b) Find the marginal density functions of X and Y (c) Calculate the probability P(X
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- Q1. Let x be a random variable with density function 2 (k+1)x 0 < x < 1 0 otherwise 9 = f(x): Find the moment generating function of x.Suppose that X, Y are jointly continuous with joint probability density function f (x, y) = ce ² (² 2 x, y = (-∞0, ∞0), for some constant c. (a) Find the value of the constant c. (b) Find the marginal density functions of X and Y.The cumulative distribution function of the continuous uniform distribution between con- stants a and b is given by F(x) = P(X ≤ x) = x-a - a x b (a) The probability density function is f(x) = F(r). Find the form of f(x). (b) Find the derivative of f(x) for x = [a, b]. Is f(x) decreasing, increasing or flat in this region? (c) Does f(x) have a single maximum in the region [a,b]? If so, what is it, or if not, why not?
- Let X be a continuous random variable with density function be-bx for a > 0 f (x) = otherwise where b > 0. - find M(t) the moment generating function of X, then what is E(x) ?Interpret the following three sets of data using scatter chart and regression analysis, using slope , intercept, Coefficient of Determiniation (R2) , regression data (using excel), 95% confidence interval, Regression and P value ,Do I reject the null hypothesis. Generate and explain the derivation of insights using regression analysis and its associated visualization. Differentiate between the signals identified by business analytics and the noise that is inherent in the system. 1.C20 (annual number of training hours) versus Y: C21 (time to serve customers in minutes) C20 100 100 100 100 100 125 125 125 125 150 150 150 150 150 175 175 175 175 C21 21.8 21.9 21.7 21.6 21.7 21.7 21.4 21.5 21.4 21.9 21.8 21.8 21.6 21.5 21.9 21.7 21.8 21.4 check_circle Expert Answer thumb_up thumb_down Step 1 X:annual number of training hour and Y:time to serve customers in minutes Steps to construct scatter plot in…Suppose that X and Y have a joint probability density 7e-2-7y if x, y ≥ 0 otherwise (a) Verify that fx.y is indeed a probability density function. function given by fx.x (x, y)
- Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 0Let X and Y have joint density function fxy (x, y) = x + y for 0Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x)= = 0 x² 25 1 X 4.5). 5≤X Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 4), (b) Calculate P(3.5 ≤ x ≤ 4). (d) What is the median checkout duration ? [solve 0.5 = F(p)].4) It has been determined that the probability density function for the wait in line at a counter is given by, So f(t) = if t 0 a) Verify that this is in fact a probability density function. b) Determine the probability that a person will wait in line for at least 6 minutes. c) Determine the mean wait in line.Suppose that the random variables Y1 and Y2 have joint probability density function, f(y1, y2), given 6y y2, 0syı < y2, y1 + y2 < 2 fV1, y2) = - 0, elsewhere Derive the marginal density of Y1. Derive the marginal density of Y2.(Hint: this will have to broken down into two parts!!!) Derive the conditional density of Y2 given Y1 = y1. Find P(Y2 < 1.1 | Y1 = .60). %DLet X and Y have the joint probability density function fxy(x, y) = {#², for 0SEE 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