Let Y, and Y2 have a joint density function given by [3y1 0 < y2 < y1 S 1 elsewhere. 3.1.3. Let Y, and Y, denote random variables. Use the formula E (Y,) = E[E(Y,|Y½)] to find E (Y2). " 3.1.4. Use the marginal density function of Y2 to find E(Y2) to verify the answer in (3.1.3.).
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- Please help with this question fast.5. A continuous random variable X that can assume value between x-2 and x-5 has a density function given by 1+x f(x) = 8 a. Show that P(2Q2. Here, the joint density function of two random variable X and Y are, S(2,9) = {clE*y* 3y² + x²y³), 110. The density function for a random variable X is given by J / x + k (a) Find k. (c) Find u. f(x) = if 2 ≤ x ≤4 otherwise (b) Find P(X> 2.5). (d) Find P(2 < X < μ).Q 4.2. Let (X, Y) be a random variable with the following density: 15x²y 0 0 < x < y < 1, otherwise. fx,y(x, y) = { { 1. Express E(YX) in terms of X. 2. Express Var(X|Y) in terms of Y.Let Y1, Y2, ..., Yn denote a random sample of size n from a population whose density is given by 3y2 0 < y< 0, f (y|0) = өз 0, elsewhere. 1.1. Show that Y(n) max(Y1, Y2, ... , Yn) is sufficient for 0.6. The random variable X is distributed by f(z)=e, z>0. What is the density, g(y), of where it is non-zero? A. 1 X²¹ 2y³/2 B. 2√9 C. 29-√7 D). -1/47 -1/ E. eLet X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x (Ə ln(f(X;0) nE5. Let X be a random variable whose density is given by the formula cx? if x E (0, 2) f (x) = otherwise. (a) Find c. (b) Let Y be the integer part of X, i.e., Y = 0 if 0 < X < 1 and Y = 1 if 13.18 A continuous random variable X that can as- 5 has a density sume values between x = 2 and x = function given by f(x) = 2(1+x)/27. Find (a) P(X < 4); (b) P(3 ≤ X < 4). 3.19 For the density function of Exercise 3.17, find F(x). Use it to evaluate P(2 < X < 2.5). 3.20 For the density function of Exercise 3.18, find F(x), and use it to evaluate P(3 ≤ X < 4).46. Given that X has a density function 2x 3- x f (x) = for 05) For the following density function f(x) = c x2 (1–x), 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