1. Find the population covariance between X and Y .2. Find E[Y |X = x].3. Find Var[Y |X = x]. Let X and Y be random variables with joint pdffx,y (x, y)8xyfor 0 < x < y < k,where k is a positive constant.

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Answered: Let X and Y be random variables with…

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Let X and Y be random variables with joint pdf 8xy for 0 < x < y < k, k4 > fx,y (x, y) where k is a positive constant.

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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1. Find the population covariance between X and Y .
2. Find E[Y |X = x].
3. Find Var[Y |X = x].

Let X and Y be random variables with joint pdf
fx,y (x, y)
8xy
for 0 < x < y < k,
where k is a positive constant.

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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