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- 1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.The random variables X and Y have ä joint Probability masS 6 function as Follows - (X.Y); For ( X,Y) E A 18 For the other (x,Y) while A = {(x,Y ,2,3 end y=l,2} ore Depine: %3D a The probability mass Function For the random variable V= X+ Y b) The probability mass Function For the random variable V= X-Y 285The random variable Y is defined by Y = - (X + \X1), where X is another RV. %3D Determine the density and distribution function of Y in terms of those of X. 44
- 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.Q27. Statiçally independent random variables X and Y have respective densities, f,(x) = 5u(x) exp(-5x) af,(y) = 2u(y) exp(-2y), find the density of the sum W = X+ Y.The PDF of a random variable Y is Sy/2 02. Let X and Y denote independent random variables with respective probability density func- tions fx(x) = 2x, 04. Find the average value of the sum of the squares of two numbers x and y where (b) x + y| < 1 and x - y| < 1.Consider a random variable Y with density S (1/2)(y + 1), -1 < y < 1, else. f(y) Calculate E(W) and V(W) for the random variable W = 4+Y – 2Y².Q 4.2. Let (X, Y) be a random variable with the following density: {152-2 0 £x,x (x, y) = { 1. Express E(Y|X) in terms of X. 2. Express Var(XY) in terms of Y. 0 < x < y < 1, otherwise.5. 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 1tEx. 4. Let X,Y are independent random variables where X ~ N(0, 1) and Y ~ G(1/2, n/2). Let T:= X//Y/n, then show that the density function of T is described as r(n+1)/2) (1+) VnnI'(n/2) -(n+1)/2 fr(t) - (-∞SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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