(f) Consider the pair of discrete random variables X, Y with joint PMF described below: 3 У Px,y(x, y) 0 -2 -1 +1 +2 1/12 1/6 0 x 1 1/3 0 1/6 2 1/12 1/12 1/12 Compute E[XY²] and E[Y³|X = 0].
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- Two independent random variables, X and Y, are both uniformly distributed on [0, 1]. The random variable Z is defined by Z = (X-H)² + (Y - My) ², E[X] and y E[Y]. Determine the expected value of Z. where (a) (b) = Determine the variance of Z.Consider random variables Y and X = 7Y + 9 with moment-generating functions 1 e2t – e4t 1- et ebt – emt m, (t) 2 m – b 1– ect Identify the values of the parameters (b, m, c) for X.If X and Y are Gaussian random variables then what is E[XY]?
- Let W = 2X + 5Y – 3Z, where the random variables X, Y, and Z satisfy E(X)= 2, V(X)= 5, E(Y)= -3, V(Y)=4, E(Z)=7, V(Z) = 6, Cov(X,Y) = -1, Cov(Y, Z) =3, Cov(Z, X)= 2. Calculate E(W), V (W) and Cov(W, Y).Find E(R) and V (R) for a random variable R whose moment-generating function ismR(t) = e2t(1-3t2)-1Let X and Y be random variables with joint den- √(x+2y) x,y>0,x+y Y). (b) Calculate fx y(xly). sity: f(x,y): = (c) Calculate P(X < 1 Y = 1). (d) Calculate E[X²|Y].
- The joint pdf of the random variables X and Y is given by { cx, x > 0, y > 0, 1 < x + y < 2, f (x, y) 0, elsewhere, for some constant c. (a) Draw the support of (X, Y). (b) Show that c= = 6/7.4. Continuous random variables X and Y are independent, with parameters ux = 30, ly = 40, Ox = 15, and ơy = 5. Which of the following gives the correct values for ux+Y and ox+y? = 70 and ox+y = 14.1 (A) Hx+Y (B) Мx+ү %3D 70 and o x+y %3D 15.8 (C) Hx+Y = 70 and ox+y = 20 (D) Ux+Y = -10 and ox+Y =14.1 (E) Ux+y =-10 and ox+y = 15.8The moment-generating function of the discrete random variable X is 1 M(t) =e 1 1 +. -2t 2t -3t e+ 6. . 3 What is the value of P(X> 1) ) 6.
- The joint p.d.f of two random variables X and Y is given by 1. ƒ(x, y) = = x(x − y),0 < x < 2,− x < y12 The joint pdf of 2 - random variables is X and Y is fxy (x, y) = k (6 - x - y) for 0The joint pdf of a bivariate random variable (X, Y) is given by Kxy 0SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON