How to prove that:
Cov(aX, aY) = a^2Cov(X,Y)
Answer :
Since
eq 1
Here x= average of xi
y= average of yi
Eq 2
From equation 1 and 2 it is clear that
Cov(ax,ay)=Cov(x,y)
Problem 2 Suppose two continuous random variables (X, Y) ~ f(x,y). (1) Prove E(X +Y) = E(X)+ E(Y). (2) Prove Var(X + Y) = Var(X) + Var(Y)2Cov(X, Y). (3) Prove Cov(X, Y) E(XY)- E(X)E(Y). (4) Prove that if X and Y are independent, i.e., f(x, y) Cov(X, Y) 0. Is the reverse true? (5) Prove Cov (aX b,cY + d) = acCov(X, Y). (6) Prove Cov(X, X) = Var(X) fx (x)fy(y) for any (x,y), then =
Prove, Var(ay)= a^2 var(y) Var(y+a)= var(y) Var(x+y)= var(x)+var(y)+2cov(x,y)
Prove the following statements
• corr(ax,y) = corr(x,y)
• show that if x,y and z are independent. Show what happened
to:
cov(x+y,x+z)= ?
• assume x and y are not independent:
cov(ax + b, y)= ?
70 tre la Car
Find Ay and f'(x)Ax for y=f(x) = 3x®, x= 3, and Ax=0.02. Ay = (Round to four decimal places as needed.) f'(x)Ax = (Round to two decimal places as needed.)
Prove cov(x+y,x-y) where x and y are independent.
5. Prove the following identity: ???(?, ?) = ?(??) − ????, where cov(X,Y) is the covariance between random variable X and Y, ?? is the mean of X and ?? is the mean of Y.
4. Recall that the covariance of random variables X, and Y is defined by Cov(X,Y) = E(X - Ex)(Y - EY) (a) (2pt) TRUE or FALSE (circle one). E(XY) 0 implies Cov(X, Y) = 0. (b) (4 pt) a, b, c, d are constants. Mark each correct statement ( ) Cov(aX, cY) = ac Cov(X, Y) ( ) Cor(aX + b, cY + d) = ac Cov(X, Y) + bc Cov(X, Y) + da Cov(X, Y) + bd ( )...
This Question: 1 pt For y = f(x)=2x-1, x= 3, and Ax=2 find a) Ay for the given x and Ax values, b) dy = f'(x)dx, c) dy for the given x and Ax values a) Ay = || (Round to four decimal places as needed b) dy = f'(x)dx= ( ) ox Bound to two decimal places as seeded
Given z =f(x, y) and w = g(x, y) such that a/ax = aw/ay and az/ay-みv/ar. If θι and θ2 are two mutually perpendicular directions, show that at any point FOx, y), as/as, = aw/as, and as/as, =-aw/as, . 21.
Given z =f(x, y) and w = g(x, y) such that a/ax = aw/ay and az/ay-みv/ar. If θι and θ2 are two mutually perpendicular directions, show that at any point FOx, y), as/as, = aw/as, and as/as, =-aw/as, . 21.
Give a counterexample to the claim that if ax ≡ ay mod n then x ≡ y mod n.