Let Y denote a random variable with the following density function. { c((y – 5)³ + y + 62) if 1< y < 9, otherwise. - f(y) = a. Find the value of the constant c. b. Find the CDF, F(y). c. Calculate the probability P(Y > 4|Y > 2).
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- Let X and Y be two continuous random variables with joint probability density function given by: (12x(1– x). %3D 0, otherwise Then the cov(X,Y)is: None of these -1/36 1/50What values of a, b, c, and d should be used to calculate the probability shown below? xy OSxs1 12. Let X have the probability density function: 10-12². √x f(x) = a. What is a? b. What is E(X)? C. What is Var(X)? 0, 0≤x≤ a otherwiseThe conditional probability density function of Y, given that X=x for some x>0, takes the following form: fyx=x(y) = C (x²-y²) x° e Ex, for -xX and Y are independent, X ~ U (0, 1) and Y U (0, 1). Calculate the probability P(X+Y<1.5).Let X be the proportion of new restaurants in a given year that make a profit during their first year of operation, and suppose that the density function for X is ƒ(x) = 20x³(1 − x) Find the expected value and variance for this random variable. E(X) = = Var(X) 0 ≤ x ≤ 1Let X and Y be independent Exponential (A) random variables. Let M = min{X, Y) min{X, Y} and U = max{X, Y}. 1. Compute the distribution function and probability density of M. 2. Compute the distribution function and probability density of U. 3. Compute the joint distribution function F(M,U) (x, y) of M and U, and thus deduce the joint density fM,U(x, y).f(t) = A exp ( - bt) means f (t) = Ae-bt The probability density function for the random variable T is f[t) = kt exp (-k2) for t>0 where k >0. E(T) = Select one: a. % [k/ T) b. 1/4 (T/k)/2 c. (T/k)/2 d. % (T/k)1/2Let Y denote a random variable with the following density function. 1 f (y) = { In(2)(+1) if 0Recommended 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