26)
E((Y-bX)2 ) =E(Y2+b2X2-2bXY( -E(Y2)-2bE(XY)+b2E(X2)
option 1 is correct
27)
differentiating 26 with respect to b"
2E(XY) =2b*E(X2)
b=E(XY)/E(X2)
option 5) is correct
The following relates to Problems 26 - 27. Let X, Y be random variables and b...
2. Let the random variables X and Y have the joint PDF given
below:
(a) Find P(X + Y ≤ 2).
(b) Find the marginal PDFs of X and Y.
(c) Find the conditional PDF of Y |X = x.
(d) Find P(Y < 3|X = 1).
Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
1. Let X and Y b e random variables, with μΧ = E(X), μΥ = E(Y), σ炙= Var(X) and σ Var(Y) (2) Let Ỹ be a linear function of X, ie. Ỹ = +51X where bo and bl are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ....
Let X and Y be independent identically distributed random variables with means µx and µy respectively. Prove the following. a. E [aX + bY] = aµx + bµy for any constants a and b. b. Var[X2] = E[X2] − E[X]2 c. Var [aX] = a2Var [X] for any constant a. d. Assume for this part only that X and Y are not independent. Then Var [X + Y] = Var[X] + Var[Y] + 2(E [XY] − E [X] E[Y]). e....
Let X and Y be independent identically distributed random variables with means µx and µy respectively. Prove the following. a. E [aX + bY] = aµx + bµy for any constants a and b. b. Var[X2] = E[X2] − E[X]2 c. Var [aX] = a2Var [X] for any constant a. d. Assume for this part only that X and Y are not independent. Then Var [X + Y] = Var[X] + Var[Y] + 2(E [XY] − E [X] E[Y]). e....
The following relates to Problems 21 and 22. Let X ~ NĢi 1, σ2-1), Y ~ NĢı = 2,02-9) and ρχ.Y = 0.5 (recall that ρΧΥ stands for the correlation coefficient of X and Y) Problem 21: Find COV(X, Y) and Var(X +Y) 1 COV(X, Y) 1.5 and Var(XY)-15; [2] COV(X, Y) 3 and Var(X+Y)-7; 3 COV(X,Y) 3 and Var(X + Y) 10: 4] COV(X,Y) 1.5 and Var(X + Y)-7; [5] cov (X, Y) = 1.5 and Var (X +...
Exercise 11. Let Xi,y, be random variables with joint PDF fXiXi. Let X2,Y2 be random variables with joint PDF fx2,Y2. Let T: R2R2 and let S: R2 -R2 so that ST(x, y) (z, y) and TS(a, y) (x, y) for every (x, y) E R2. Let J(x, y) denote the determinant of the Jacobian of S at (x,y. Using the change of variables formula from multivariable calculus, show that
4. Let X and Y be continuous random variables with joint density function f(x, y) = { 4x for 0 <x<ys1 otherwise (a) Find the marginal density functions of X and Y, g(x) and h(y), respectively. (b) What are E[X], E[Y], and E[XY]? Find the value of Cov[X, Y]
7. Find cov(X, Y)
8. Are the random variables X, Y independent? Justify
answer
Edit : do not solve number 1, I already solved.
C=3/32
Use this information for problems 1 -8: Let X, Y be two continuous random variables and let f(x, y)2y + xy?) over the range O< x<2 and 0< y< 2. Determine the v function alue of the constant c that makes this function a joint probability density 1.
Use this information for problems 1 -8:...
Let X and Y be two random variables such that E(X) = 2, E(Y) = 5 and E(XY)=7. The covariance of (X, Y) is equal to: a. 17 b. 14 c. 3 d. -3 a O с Od
For the random variables X and Y having E(X) = 1, E(Y) = 2, Var (X) = 6, Var (Y) = 9, and Pxy = -2/3. Find a) The covariance of X and Y. b) The correlation of X and Y. c) E(X2) and E(Y2).