1. Let X be a continuous random variable with the following density function: cx,0
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A: " Since you have posted a question with multiple sub-parts, we will solve the first three subparts…
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- Let X be a random variable with density functionf(x), with 0Q1) CDF, PDF, Expectation and Variance The cumulative distribution function (CDF) of random variable Y is y 1. a) Find the probability density function, fy(y), of random variable Y. b) Show that f fy (y)dy = 1. c) What is E[Y]? d) What is VAR[Y]?b) Let X and Y be jointly continuous random variables with the following joint density function (1/32)xy ,0 2) v. Evaluate P(Y > X – 2)If the density function of the random variable is be-bx, x >0, f(x)= 0, %D Otherwise.3. The storm runoff X (in cubie meters per second, ems) can be modeled by a random variable with the following probability density function (PDF): fa(x) = c (x -) for 0Let Y denote a random variable with the following density function. 1 f (y) = { In(2)(+1) if 0Suppose (X; Y ) is a continuous random vector with joint probability density function fx.y(x.v)= v Osxs2,01. Let X be a random number from (0, 1). Find the probability density function of Y = 1/X.A random variable X has a probability density function given by: [cx +3, -3sxs-2 f(x)={3-cx, 2sxs3 0, elsewhere 1. Find the value of c that will make the pdf valid. 2. Derive its corresponding distribution function.Recommended 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