11. Let the correlation coefficient of X and Y be ρ(X,Y)-N C XY VVar(X)VVar(Y) -p(X, Y)....

Question

Question

11. Let the correlation coefficient of X and Y be ρ(X,Y)-N C XY VVar(X)VVar(Y) -p(X, Y). (Y) Show that ρ(-3X,-2Y-a(X, Y) and ρ(X-2Y)

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Ans. Since variances as well as coavariances are independent of change of origin but depend on change of scale.

The correlation coefficient is ratio of covariance and variance, being independent of change of origin and sclae but depend on sign.

Conn (x,y) xyCov(x,y) = Van (X) Von (Y) Now Van (-3x) (-3)2 van (x) -g vorn (X) = -2)-Van ( Cov(-3x,-2y) Cov(xN) Cos (X1) Now Van (-2y) 4 van (y) = Cov (x,-2Y) Val -J(x,y)

Add a comment

Answer 2

Similar Homework Help Questions

Let ρ represent the true population coefficient of correlation of two variables X and Y ....

Let ρ represent the true population coefficient of correlation of two variables X and Y . Suppose you want to test the hypothesis that ρ = 0. Explain how you would test this hypothesis. [Hint: by the relationship between b1 and rXY ]
20, variances a,a and correlation 4. Let X. Y be normal bivariate r.v. with coefficient p....

20, variances a,a and correlation 4. Let X. Y be normal bivariate r.v. with coefficient p. a) Write what are E (X|Y), var (X|Y)? b) Show that σi + σισ E (XXY) afo(-p) +2pa 102+0 var (XXY 2) Hint. (X, XY)is normal bivariate: apply a).
4.2 The Correlation Coefficient 1. Let the random variables X and Y have the joint PMF...

4.2 The Correlation Coefficient 1. Let the random variables X and Y have the joint PMF of the form x + y , x= 1,2, y = 1,2,3. p(x,y) = 21 They satisfy 11 12 Mx = 16 of = 12 of = 212 2 My = 27 Find the covariance Cov(X,Y) and the correlation coefficient p. Are X and Y independent or dependent?

3. Suppose that (M, ρ) is a compact metric space and f : (M, p)-+ (M,p) is a function such that (Vz, y E M) ρ (z, y) ρ (f (x), f (y)). a. Let x E (M, ρ) and consider the sequence of points {f(n)...

3. Suppose that (M, ρ) is a compact metric space and f : (M, p)-+ (M,p) is a function such that (Vz, y E M) ρ (z, y) ρ (f (x), f (y)). a. Let x E (M, ρ) and consider the sequence of points {f(n) (X)}n 1 . (Remember: fn) denotes the composition of f with itself, n times, so for each n, f+() rn, k E N) such that ρ (f(m) (x) ,f(n +k) (r)) < ε ....
56. Let S = N × N and let ρ be a binary relation on şdefined...

56. Let S = N × N and let ρ be a binary relation on şdefined by (x,y)ρ(z, w)艹x + y-z + w. Show that p is an equivalence relation on S and describe the resulting equivalence classes.
Let X and Y have the following joint distribution X/Y 0 1 0 0.4 0.1 1...

Let X and Y have the following joint distribution X/Y 0 1 0 0.4 0.1 1 0.1 0.1 2 0.1 0.2 a) Find Cov(4+2X, 3-2Y) b) Let Z = 3X-2Y+2 Find E[Z] and σ 2Z c) Calculate the correlation coefficient between X and Y. What does this suggest about the relationship between X and Y? d) Show that for two nonzero constants a and b Cov(X+a, Y+b) = Cov(X,Y)

4.7 Let r'n be the Pearson correlation coefficient from a sample size of n. It is...

4.7 Let r'n be the Pearson correlation coefficient from a sample size of n. It is known that rn is asymptotically distributed as N (p, (1 – p2)2/n), where p is the population correlation coefficient. Show that Fisher's Z-transformation Z = { In((1 + ra)/(1 – in)) is actually a variance-stabilizing transformation.
(a) Find the correlation coefficient ρX,Y . (b) Are X and Y independent? Explain why. Let...

(a) Find the correlation coefficient ρX,Y . (b) Are X and Y independent? Explain why. Let (X, Y) have joint pdf given by 0 y 00, ey f(x, y) 0, o.w., (a) Find the correlation coefficient px,y. (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
6.72 Let Y =X+N where X and N are independent Gaussian random variables with different variance and N is zero mean. (a) Plot the correlation coefficient between the “observed signal” Y and the “desire...

6.72 Let Y =X+N where X and N are independent Gaussian random variables with different variance and N is zero mean. (a) Plot the correlation coefficient between the “observed signal” Y and the “desired signal” X as a funtion of the signal-to-noise ratio (b) Find the minimum mean square error estimator for X given Y (c)Find the MAP and ML estimators for X given Y (d) Compare the mean square error of the estimators in parts a, b, and c.

5. Let X1,X2, . , Xn be a random sample from a distribution with finite variance. Show that (i) COV(Xi-X, X )-0 f ) ρ (Xi-XX,-X)--n-1, 1 # J, 1,,-1, , n. OV&.for any two random variables X and Y)...

5. Let X1,X2, . , Xn be a random sample from a distribution with finite variance. Show that (i) COV(Xi-X, X )-0 f ) ρ (Xi-XX,-X)--n-1, 1 # J, 1,,-1, , n. OV&.for any two random variables X and Y) or each 1, and (11 CoV(X,Y) var(x)var(y) (Recall that p vararo 5. Let X1,X2, . , Xn be a random sample from a distribution with finite variance. Show that (i) COV(Xi-X, X )-0 f ) ρ (Xi-XX,-X)--n-1, 1 # J,...

11. Let the correlation coefficient of X and Y be ρ(X,Y)-N C XY VVar(X)VVar(Y) -p(X, Y)....

Homework Answers

Add Answer to:
11. Let the correlation coefficient of X and Y be ρ(X,Y)-N C XY VVar(X)VVar(Y) -p(X, Y)....

Post as a guest

Earn Coins

Let ρ represent the true population coefficient of correlation of two variables X and Y ....

20, variances a,a and correlation 4. Let X. Y be normal bivariate r.v. with coefficient p....

4.2 The Correlation Coefficient 1. Let the random variables X and Y have the joint PMF...

3. Suppose that (M, ρ) is a compact metric space and f : (M, p)-+ (M,p) is a function such that (Vz, y E M) ρ (z, y) ρ (f (x), f (y)). a. Let x E (M, ρ) and consider the sequence of points {f(n)...

56. Let S = N × N and let ρ be a binary relation on şdefined...

Let X and Y have the following joint distribution X/Y 0 1 0 0.4 0.1 1...

4.7 Let r'n be the Pearson correlation coefficient from a sample size of n. It is...

(a) Find the correlation coefficient ρX,Y . (b) Are X and Y independent? Explain why. Let...

6.72 Let Y =X+N where X and N are independent Gaussian random variables with different variance and N is zero mean. (a) Plot the correlation coefficient between the “observed signal” Y and the “desire...

5. Let X1,X2, . , Xn be a random sample from a distribution with finite variance. Show that (i) COV(Xi-X, X )-0 f ) ρ (Xi-XX,-X)--n-1, 1 # J, 1,,-1, , n. OV&.for any two random variables X and Y)...

11. Let the correlation coefficient of X and Y be ρ(X,Y)-N C XY VVar(X)VVar(Y) -p(X, Y)....

Homework Answers

Add Answer to: 11. Let the correlation coefficient of X and Y be ρ(X,Y)-N C XY VVar(X)VVar(Y) -p(X, Y)....

Post as a guest

Earn Coins

Add Answer to:
11. Let the correlation coefficient of X and Y be ρ(X,Y)-N C XY VVar(X)VVar(Y) -p(X, Y)....