Let the joint density function of X and Y be given by e-(u+÷) for 0 < x, y < ∞0, fx,y (x, y) : otherwise. (a) Byfinding the margina ucnSity jY (9), oNOW (b) (i) Fo , dotowmino S(), the conditional density of X aiven hat V Emplain without caleulation) why for 1. (ii) Caicuiale Te (c) Given that E[X] = 1 and E[Y] = 1, show that Cov(X,Y) = 1. %3D %3D Comment on the relationship between the variables X and Y.

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Probability. Only question c. 

Let the joint density function of X and Y be given by
e-(s+;)
for 0 < x, y < ∞,
fx,y (x, y) :
otherwise.
(a) S ng the magmarathsiy JY (9), oOW a
(b) (i) Fo dotormine f() the conditional density of X aiven
that V
Explain without caleulation why for
-רדקיר
Honoo, ur other wio, obow that BvÀ 1.
(ii) CaicuialeTE |T
(c) Given that E[X] = 1 and E[Y] = 1, show that Cov(X, Y) = 1.
Comment on the relationship between the variables X and Y.
Transcribed Image Text:Let the joint density function of X and Y be given by e-(s+;) for 0 < x, y < ∞, fx,y (x, y) : otherwise. (a) S ng the magmarathsiy JY (9), oOW a (b) (i) Fo dotormine f() the conditional density of X aiven that V Explain without caleulation why for -רדקיר Honoo, ur other wio, obow that BvÀ 1. (ii) CaicuialeTE |T (c) Given that E[X] = 1 and E[Y] = 1, show that Cov(X, Y) = 1. Comment on the relationship between the variables X and Y.
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