The joint PDF of two jointly continuous random variables X andY is c(x² + y²) for 0 < x < 1 and 0 < y< 1, fxy(x, y) otherwise. c = 3/2. E(Y) = 5/8. Show that X and Y are negatively correlated.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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The joint PDF of two jointly continuous random variables X and Y is
S c(a? + y?) ,
for 0 < x <1 and 0 < y < 1,
fx,x(x, y)
‚Y
otherwise.
c = 3/2.
E(Y) = 5/8.
Show that X and Y are negatively correlated.
Transcribed Image Text:The joint PDF of two jointly continuous random variables X and Y is S c(a? + y?) , for 0 < x <1 and 0 < y < 1, fx,x(x, y) ‚Y otherwise. c = 3/2. E(Y) = 5/8. Show that X and Y are negatively correlated.
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