9 0/1 point (graded) Let X be distributed uniformly over 1,1, andlet y- Xw.p. 3/4, l-X...
0/1 point (graded) Let X be distributed uniformly over {-1 { Xw.p. 3/4, where w.p. means "with probability". Find Cov (X, Y) , 1f, and let Y- X w.p. 1/4., 2 Submit You have used 1 of 4 attempts Reset
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)
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...
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.
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 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 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)
(iv) Let X be exponentially distributed with parameter 1 and let Y be uniformly distributed in the interval [0, 1]. Using convolution, find the probability distribution function of
Exercise 6.34. Let (X,Y) be a uniformly distributed random point on the quadri- lateral D with vertices (0,0), (2,0), (1,1) and (0,1). (a) Find the joint density function of (X,Y) and the marginal density functions of X and Y. (b) Find E[X] and E[Y]. (c) Are X and Y independent?