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- The joint density function of Y1 and Y2 is given byf(y1, y2) = (y1 + y2, 0 < y1 < 1, 0 < y2 < 1,0, elsewherea) Find marginal density functions. Are Y1 and Y2 independent?b) Could you tell whether Y1 and Y2 were independent or not without finding marginaldensity functions? Explain.c) Find P(Y1 + Y2 < 0.2).d) Find P(0 < Y2 < 0.5|Y1 = 0.4).For x1, the marginal distribution fx1 (x1) function is validis it a density function)Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Find the marginal fx(x) and fy(y). Show if f(x,y) dependent. Compute mean(x), mean(y), variance (x) and variance(y)
- Let denote the amount of gasoline stocked in a bulk tank at the beginning of a week, and let Y denote the amount sold during the week. Then Z = X- Y represents the amount leftover at the end of the week. Assume that and Y have the joint density 024. Consider a distribution with density on the interval [0, 2]. Let the probability density function (pdf) for this distribution be the following: fy(u) = % on [0, 2] 2 (i) Draw/plot the pdf fy(y) vs. y for the interval [0, 2]. (ii) Determine the Cumulative Distribution Function (CDF), F, (y). (iii) Draw/plot the CDF F,(y) vs y for the interval [0, 2]. (iv) Determine the expected value of the Random Variable (RV) y, i.e., E [y].Let X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.Find the mean and standard deviation for each uniform continuous model U(1, 13) U(70, 200) U(3, 92)4. What are the median, and mode, respectively, for the density function f(x) = Ta (1 + x²)'The time T a business is closed after a fire has the cumulative distribution function (부)- 3 1 1 F7(t) = t>0 t+1 otherwise = VT. The cost to the insurer is X = Determine the density of X for x > 0.7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 0The joint probability density function of two dimensional random variable(X,Y) is given 8 by f(x, y) = xy, 13xsys2 9 = 0, elsewhere Find the marginal density functions of X and Y.Suppose that X and Y have a joint probability density function given by ce-3z=5y if a, y 20 fx.y(T, y) = otherwise Find the marginal probability density function fx and state the name of the distribution of X.SEE 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