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 0.09Suppose 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.The 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. 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.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.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 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, 0C2. 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.= 10. We do Let X and Y be statistically independent random variables with Var(X) = 4 and Var(Y) not know E[X] or E[Y]. Let Z = 2X +9Y. Calculate the correlation coefficient defined as p(X, Z) = Cov(X,Z) √Var(X)Var(Z)SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON