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- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .Normal distribution. The moment generating function of a random variable U is M(t) = (1 - 8t)^-7. Find: i)Probability density function, ii)Mean, iii)Variance of U.
- A random variable x follows continuous uniform distribution on the interval [18,38]. Find the variance V ar (X). Answer should be with 2 decimal places.Let X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysxX is a normally normally distributed variable with mean µ = 30 and standard deviation o = 4. Find a) P(x 21) c) P(30 < x < 35)Suppose that X ~ and variance 1, i.e., (Y X = x) ~ N(2x, 1). Find the marginal pdf of Y. N(0,1). Then, under the condition X = x for some r E R, the distribution of Y is normal with mean 2xThe discrete random variable X has probability mass function kx x = 2,3 2kx P(X = x) = x = 4,5 x-1' 0,otherwise. Find the variance of X.6) Allow a continuous probability distribution to be defined as f(x) = 4x³ for the range 0 sxs1. Demonstrate that the area underneath the curve is 1 (the function integrates to 1) and calculate the mean and variance of the probability distribution.The number of daily visitors to a website (X) has a normal distribution with an average value of u=200 and a standard deviation of 50, and Z is a standard normal variable, so: P( X < 150)= P(Z < 1,0) /other P(X < 150)= P(Z< -1,0) P( X < 150) = P(Z > - 1,0)2) Let X be a continuous random variable with PDF 0Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isSEE 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