25. The random variables X and Y have the joint probability function f(x, y) = K(4- x- y); 0
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- The joint probability function of two discrete random variables X and X is given by f(x, y) = cxy for x = 1, 2, 3 and y = 1, 2, 3, and equals zero otherwise. Find (a) the constant c, (b) PCX = 2, Y = 3), (c) P(1 ≤X ≤ 2, Y ≤ 2), (d) P(X22), (e) P(Y ). (c) P ¹). (c) P ( < X < ³), (d) P(Y < ¹), (e) whether X and Y are independent. dix dy C CXUsing 2 independent DRVS X and Y with probability distribution px(x) and py (y) below, find E(Z) where Z = X + Y X 1 2 3 4 Px(x) 1/8 3/16 3/8 3/16 1/8 Y 3 4 5 Py(y) 1/4 1/4 1/4 1/4Asap
- Given that random variable X is continuous type , we form the random variable Y as Y = g (x) = 6 F, (x) + 4. Then f, (y) is %3D ON(6, 4) ON (4, 6) O U (4, 10) OU (6, 10)2. Let X and Y be random variables, and let a and b be constants. (a) Starting from the definition of covariance, show that Cov(aX,Y) = a Cov(X,Y). You may find it helpful to remember that if EX = µx, then EaX = aux. (b) Show that Cov(X + b, Y) = Cov(X,Y). Now let X, Y, Z be independent random variables with common variance o?. (c) Find the value of Corr(2X – 3Y + 4, 2Y – Z – 1). You may use any facts about covariance from - the notes, including those from parts (a) and (b) of this question, provided you state them clearly.Find var(Y)
- Q2) The joint probability function of two discrete random variables X and Y is given by fx,y) = c(2x+y),where x and y can assume all integers such that 0 sIS2,0s ys3,and fx,y) = 0 otherwise. (a) Find the value of the constant c (b) Cov (X, Y), (c) p.(1) Let X = b(16, -) find E(4-3x) and distribution function. (2) Let X be a random variable with p.d.f. -2 kx 1-) Suppose X and Y are continuous random variables. The range of X is [1,3], the range of Y is [0, 1]. The joint pdf of X and Y be given by f(x, y) = 2xy³ - 2y³. Verify if X and Y independent random variables.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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