Answered: 65. Consider the jointly continuous… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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Question

65. Consider the jointly continuous random variables from homework questions 59-62 with joint pdf:
f(x, y) = 12xyI(0,1)(x) I(0,z²) (y)
(a) Find the covariance of X and Y.
(b) Find the correlation between X and Y.

For questions 59-62, consider the following experiment:
Suppose the location of a particle in the plane is restricted to be within the region of the first quadrant
enclosed by y = 0, y = x², and x = 1 and that the x- and y- coordinates of the point are described by
the jointly continuous random variables X and Y, respectively, with joint pdf
f(x, y) = axyI(0,1)(x) I (0,z²) (y)

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