Homework Answers
TOPIC:Covariance of random variables.
![Now, we have, yal * ; w. p. C-X ; wop. 4 Sx; wip. 2 -x ; w. p. I -*&& {-1,1]. Then, we have E (x1). - [E (* Y!x=2]. T: We kno](http://img.homeworklib.com/questions/c25927e0-6f05-11ea-9b4b-17131759c128.png?x-oss-process=image/resize,w_560)
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0/1 point (graded) Let X be distributed uniformly over {-1 { Xw.p. 3/4, where w.p. means...
9 0/1 point (graded) Let X be distributed uniformly over 1,1, andlet y- Xw.p. 3/4, l-X...
9 0/1 point (graded) Let X be distributed uniformly over 1,1, andlet y- Xw.p. 3/4, l-X w.p. 1/4, where w.p. means "with probability". Find Cov (X,Y) 2 Submit You have used 1 of 4 attempts
Example of Covariance II 4 points possible (graded) Let X, Y be random variables such that...
Example of Covariance II 4 points possible (graded) Let X, Y be random variables such that • X takes the values +1 each with probability 0.5 . (Conditioned on X) Y is chosen uniformly from the set {-3X - 1,-3x, -3x+1}. (Round all answers to 2 decimal places.) What is Cov(x,x) (equivalent to Var (X))? Cov(X, X) = What is Cov(Y,Y) (equivalent to Var (Y))? Cov(Y,Y)= What is Cov(X,Y)? Cov(X,Y)= What is Cov(Y,X)? Cov(Y,X)= Submit You have used 0 of...
5. Let (X, Y) be a uniformly distributed random point on the quadrilateral D with vertices...
5. Let (X, Y) be a uniformly distributed random point on the quadrilateral D with vertices (0,0), (2,0),(1,1), (0,1) Uniformly distributed means that the joint probability density function of X and Y is a constant on D (equal to 1/area(D)). (a) Do you think Cov(X, Y) is positive, negative, or zero? Can you answer this without doing any calculations? (b) Compute Cov(X, Y) and pxyCorr(X, Y)
0/1 point (graded X, Y have the joint probability density function f (z,y)-1 , 0 < z < 1, z < y <...
0/1 point (graded X, Y have the joint probability density function f (z,y)-1 , 0 < z < 1, z < y < z + 1 . Please enter a number. Cov (X,Y) SubmitYou have used 2 of 3 attempts Save Incorrect (O/1 point) 1 point possible (graded) x ~ f(z) 2be-HA, z є R, b > 0 and Y-sign (X) Cov (X, Y)- SubmitYou have used 0 of 3 attempts Save We were unable to transcribe this image
0/1...
Let X,Y be uniformly distributed in the rectangle defined by −3 < x−y < 3, 1...
Let X,Y be uniformly distributed in the rectangle defined by −3
< x−y < 3, 1 < x + y < 5. Find the marginal density
fX(x) and E(Y|X).In the same situation find Cov(X,Y ).
(3) Let X, Y be uniformly distributed in the rectangle defined by -3 < x-y<3, Find the marginal density fx(x) and E(Y|X). In the same situation find Cov(X, Y). 1<x+y<5.
3. A point (X, Y) is uniformly distributed on the unit square (0, 1]2. Let 0...
3. A point (X, Y) is uniformly distributed on the unit square (0, 1]2. Let 0 be the angle between the r-axis and the line segment that connects (0,0) to the point (X, Y). Find the expected value El9] (Hint: recall that conin 0 and an
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in ...
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0
(5 points) Let X be a Unif(-4, 4) variable, that is, X is Uniformly distributed over...
(5 points) Let X be a Unif(-4, 4) variable, that is, X is Uniformly distributed over the interval (-4,4) Provide answers to the following to two decimal places Part a) Find the MGF of X, evaluated at the point = 1.52. 35.9397 Part b) Let Xi,X2,... , X, be independent Unif(-4,4) variables. Let Find the MGF My(t) of Y. Evaluate the MGF at the point t 0.38 in the case n 5 6.02326 Part c) Find the standard deviation of...
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean...
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean and variance of X. (2) Let Y 2X+3. Draw the PDF of Y [8 marks] 6 marks] [8 marks (3) Find the mean and variance of Y
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y...
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0<x<1 (a) Specify the joint pdf fxy(x,y) and sketch its region of support Ω XY. (b) Determine fxly(x1025). (c) Determine the probability P(X〈2Y). (d) Determine the probability P(X +Y 1)
9 0/1 point (graded) Let X be distributed uniformly over 1,1, andlet y- Xw.p. 3/4, l-X w.p. 1/4, where w.p. means "with probability". Find Cov (X,Y) 2 Submit You have used 1 of 4 attempts
Example of Covariance II 4 points possible (graded) Let X, Y be random variables such that • X takes the values +1 each with probability 0.5 . (Conditioned on X) Y is chosen uniformly from the set {-3X - 1,-3x, -3x+1}. (Round all answers to 2 decimal places.) What is Cov(x,x) (equivalent to Var (X))? Cov(X, X) = What is Cov(Y,Y) (equivalent to Var (Y))? Cov(Y,Y)= What is Cov(X,Y)? Cov(X,Y)= What is Cov(Y,X)? Cov(Y,X)= Submit You have used 0 of...
5. Let (X, Y) be a uniformly distributed random point on the quadrilateral D with vertices (0,0), (2,0),(1,1), (0,1) Uniformly distributed means that the joint probability density function of X and Y is a constant on D (equal to 1/area(D)). (a) Do you think Cov(X, Y) is positive, negative, or zero? Can you answer this without doing any calculations? (b) Compute Cov(X, Y) and pxyCorr(X, Y)
0/1 point (graded X, Y have the joint probability density function f (z,y)-1 , 0 < z < 1, z < y < z + 1 . Please enter a number. Cov (X,Y) SubmitYou have used 2 of 3 attempts Save Incorrect (O/1 point) 1 point possible (graded) x ~ f(z) 2be-HA, z є R, b > 0 and Y-sign (X) Cov (X, Y)- SubmitYou have used 0 of 3 attempts Save We were unable to transcribe this image
0/1...
Let X,Y be uniformly distributed in the rectangle defined by −3
< x−y < 3, 1 < x + y < 5. Find the marginal density
fX(x) and E(Y|X).In the same situation find Cov(X,Y ).
(3) Let X, Y be uniformly distributed in the rectangle defined by -3 < x-y<3, Find the marginal density fx(x) and E(Y|X). In the same situation find Cov(X, Y). 1<x+y<5.
3. A point (X, Y) is uniformly distributed on the unit square (0, 1]2. Let 0 be the angle between the r-axis and the line segment that connects (0,0) to the point (X, Y). Find the expected value El9] (Hint: recall that conin 0 and an
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0
(5 points) Let X be a Unif(-4, 4) variable, that is, X is Uniformly distributed over the interval (-4,4) Provide answers to the following to two decimal places Part a) Find the MGF of X, evaluated at the point = 1.52. 35.9397 Part b) Let Xi,X2,... , X, be independent Unif(-4,4) variables. Let Find the MGF My(t) of Y. Evaluate the MGF at the point t 0.38 in the case n 5 6.02326 Part c) Find the standard deviation of...
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean and variance of X. (2) Let Y 2X+3. Draw the PDF of Y [8 marks] 6 marks] [8 marks (3) Find the mean and variance of Y
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0<x<1 (a) Specify the joint pdf fxy(x,y) and sketch its region of support Ω XY. (b) Determine fxly(x1025). (c) Determine the probability P(X〈2Y). (d) Determine the probability P(X +Y 1)
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