proof that Question 2: Let X and Y be any two random variables and let a...
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....
= Var(X) and σ, 1. Let X and Y be random variables, with μx = E(X), μY = E(Y), Var(Y). (1) If a, b, c and d are fixed real numbers, (a) show Cov (aX + b, cY + d) = ac Cov(X, Y). (b) show Corr(aX + b, cY +d) pxy for a > 0 and c> O
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....
2. Let X and Y be two random variables with a joint distribution (discrete or continuous). Prove that Cov(X,Y)= E(XY) - E(X)E(Y). (15 points) 3. Explain in detail how we can derive the formula Var(X) = E(X) - * from the formula in Problem 2 above. (Please do not use any other method of proof.) (10 points)
Stuck on this problem any help would be great thank you 12. Let X and Y be two random variables and define I X Y T= SD(X) SD(Y): (a) Show that Var(T) = 2 – 2Corr(X,Y).
How to slove it Question 5. Let X and Y be random variables having expected value 0 and correlation p. Show that E Var(Y|X)| < (1 -β)Var(Y).
Let X and Y be two independent random variables. Show that Cov (X, XY) = E(Y) Var(X).
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....
Please do by hand. Thanks in advance. 2. Let X and Y be two random variables. If Var(X) = 4, Var(Y) = 16, and Cov(X,Y) = 2, then what is Var(3Y - 2x)?
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....