9. (25 points) Let X and Y be a random variables of the continuous type having the joint pdff(x, y) = 8xy,%3D(a) [10 points] Find fa(1) and fy(y).(b) [15 points] Find Cov(X,Y) and correlation coefficient.

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Answered: 9. (25 points) Let X and Y be a random…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x) mean (y) variance (x) variance(y)
Let X and Y have joint PDFfX,Y (x, y) = 3x^2y + 3xy^2 if 0 < x < 1, and 0 < y < 1 0 otherwise.a) Find the covariance of X and Y .b) Find Var(X).c) Find the correlation of X and Y (X and Y have the same variance.)
The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanation
Suppose that Y₁ and Y₂ are uniformly distributed over the triangle shaded in the accompanying figure. 3₂ (0, 1) (-1,0) (a) Find Cov(Y₁ Y₂). Cov(Y₁, Y₂) = (b) Are Y₁ and Y₂ independent? Yes O No (1, 0) (c) Find the coefficient of correlation for Y₁ and Y₂. P= y/₁ (d) Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not? O Even though Cov(Y₁Y₂) # 0, Y₁ and Y₂ are not necessarily dependent. Since Cov(Y₁ Y₂) # 0, we should expect Y₁ and Y₂ to be dependent. O Since Cov(Y₁, Y₂) = 0, we should expect Y₁ and Y₂ to be independent. O Even though Cov(Y₁Y₂) = 0, Y₁ and Y₂ are not necessarily independent.
Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .
F(x,y) = { (x+y)/42 ; x = 1,2,3 y = 1,2 0; elsewhere ] (i) Find the mean for the random variable X. (ii) Find the mean for the random variable Y. (iii) Find the covariance Cov[X,Y]
The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) = 504, Sum (x)^2 = 47995, Sum (y)^2 = 32954, and Sum (xy) = 395650 0.255 0.147 0.855 0.174
Use the formula to calculate the linear correlation coefficient for data with the following summary statistics:
X is a discrete uniform (1,3) random variable. When X=x, Y is discrete uniform (1,x). (a) Find the correlation of X and Y (b) Find the mean value of X when Y=2.
Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.
Two random variables X = (1,2) and Y= (-2,-1] are equiprobable and independent. Determine the correlation factor r(X,Y),
Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the following to two decimal places (if applicable). (a) Coefficient of correlation p(X,Y) 0.694 (b) Var(3X+Y+1) 9.57 (c) Cov(-2Y, 3X+Y+1) (d) p(-2Y, 3X+Y+1)

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