Suppose that X and Y have the following joint probability density function. f (x, y) = 3x 400 0 < x < 6, y > 0, x − 4 < y < x + 4 (a) Find E(XY). (b) Find the covariance between X and Y.
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Suppose that X and Y have the following joint probability density function. f (x, y) =
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(a) | Find E(XY). |
(b) | Find the |
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- Value of Y 14 22 30 40 65 0.02 0.05 0.10 0.03 0.01 Value of X 5 0.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 0.09The random variable Xi , i = 1, 2, models the proportion of type i switches on a panel that are turned off during a training exercise. The joint probability density function of X1 and X2 is (attached): Find the Covariance of (X1 , X2).Suppose that X and Y have the following joint probability density function. f(x, y) = ₁34y, 0 0, x − 2 < y < x + 2 154, (a) Find E(XY). (b) Find the covariance between X and Y. Round your answer to 4 decimals. Round your answer to 4 decimals.
- Suppose that X and Y have the following joint probability density function. 3 X, 0 0, x −4 < y < x +4 400 f(x, y) = (a) Find E(XY). (b) Find the covariance between X and Y.Fill out the table giving the joint and marginal PMFs for X and Y. Find E[X] and E[Y]. Find the covariance of X and Y. Are X and Y independent?Suppose that X and Y have the following joint probability density function. f(x,y) = 134² 0 0, x − 2 < y < x+2 (a) Find E(XY). (b) Find the covariance between X and Y.
- Suppose X and Y have joint probability density function f(x, y) = { 0(a C(x² + y²), if 0Suppose X and Y have joint probability density function f(x, y) = {C(a C(x² + y²), if 0 < x < y < 1, otherwise. 0, (a) Find the value of the constant C. (b) Find the variance of X.= B1. Let X₁ and Y; be random variables with Var(X;) = o² and Var(Y₂) o for all ie {1,...,n}. Assume that each pair (X₁, Y;) has correlation Corr(X, Y) = p, but that (X₁, Y₂) and (X₁, Y;) are independent for all i j. (a) What is Cov(X₁, Yi) in terms of Ox, Oy (b) Show that Cov(X₁,Y) = poxoy/n, where Y is the average of the Y₁. (c) Determine Cov(X, Y). and p?Let 3x2, 0Let X, Y, and Z be random variables, and let Cov(⋅,⋅) denote the covariance operator as usual. Suppose that the variance of X is 0.7, Cov(X,Y) = 0.4, Cov(X,Z) = 1.2, and Cov(Y,Z) = 0.8. Find each of the following to two decimal places. (a) Cov(3Y, 3X) (b) Cov(3Y + 3, 3X + 8Z)C2. Let X and Y be random variables, and let a and b be constants. (a) Starting from the definition of covariance, show that Cov(aX, Y): = a Cov(X, Y). You may find it helpful to remember that if EX = µx, then EaX = αμχ· (b) Show that Cov(X + b, Y) = Cov(X, Y). Now let X, Y, Z be independent random variables with common variance o². (c) Find the value of Corr(2X - 3Y + 4, 2Y – Z - 1). You may use any facts about covariance from the notes, including those from parts (a) and (b) of this question, provided you state them clearly.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON