QUESTION 5 Assume that the joint density function of X and Y is given by: fxr (x, y) = { e-(x+y) 0, , x, y > 0 elsewhere; Find the probability density function of (X-Y).
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- A continuous random variable that can assume values between X = 2 and X 5 has a density function given by fx (x) = K (I +x). Find p (3 < X < 4)Let X be a random variable having density function f(x) Sex x ≥ 0 to Find a) E(X), E (X²) and E[(X− 1)²] b) Var (X) and ox otherwiseConsider the random variable X with PDFf(x) = e−x / (1 + e−x)2 , x ∈ R.Find the density function of Y = 1/ (1 + e−X)
- Let X and Y have the following joint probability density function: fX,Y(x,y) = 1 / (x2 y2), for x>1, y>1 0, otherwise Let U = 5 X Y and V = 8 X. In all question parts below, give your answers to three decimal places (where appropriate). (a) The non-zero part of the joint probability density function of U and V is given by fU,V(u,v) = A vB uC for some constants A, B, C. Find the value of A.Suppose random variable X has a density function f ( x ) = { 2 /x 2 , 1 ≤ x ≤ 2 0 , o t h e r w i s e . Then E[X4] =?Suppose that X and X, have joint probability density function x2, if 1< xı < 2 and 1 < r2 < 3 10, fx1.x.("1, 2) = otherwise. What is the joint probability density function fy,y, of Y1 = X1/X2 and Y, = X2?Suppose that X, Y are jointly continuous with joint probability density function f (x, y) = ce ² (² 2 x, y = (-∞0, ∞0), for some constant c. (a) Find the value of the constant c. (b) Find the marginal density functions of X and Y.Help me pleaseRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,