Question
Asked Sep 14, 2019

Please, help me with very detailed and self-explanatory solutions to (b) and (c) thank you

 

Exercise 2. Answer the following
Suppose X, Y) is a continuous random vector having PDF f. Say for each of the
following definitions of f whether X and Y are independent or not.
(a) f(x, y) 4xy, 0 x < 10 y < 1 and
f(x, y)8y 0 < x < y< 1
(b) f(x, y)144(x - 1/2)2, ( 1/2)2, 0 < x < 1,0 <y < 1 and
f(x, y)288(x -1/2)2, (Y 1/2)2 0 < < y< 1, 0 <y1
(c) Let (X, Y) be a point that is uniformly distributed on a square whose cor-
(1, 1Determine the marginal pdf of Y.
ners are
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Exercise 2. Answer the following Suppose X, Y) is a continuous random vector having PDF f. Say for each of the following definitions of f whether X and Y are independent or not. (a) f(x, y) 4xy, 0 x < 10 y < 1 and f(x, y)8y 0 < x < y< 1 (b) f(x, y)144(x - 1/2)2, ( 1/2)2, 0 < x < 1,0 <y < 1 and f(x, y)288(x -1/2)2, (Y 1/2)2 0 < < y< 1, 0 <y1 (c) Let (X, Y) be a point that is uniformly distributed on a square whose cor- (1, 1Determine the marginal pdf of Y. ners are

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check_circleExpert Solution
Step 1

To work out the marginal pdf's of X and Y and to decide their independence

Step 2

(b) Working out the marginal densities of X and Y

b) pdf of X frx)
=144x0.5 (y-0.5) dy
=144(x-0.5)y-0.5)
3
1
=144(x-0.5)2x-
24
-12(x-0.5)similar for f(y)
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b) pdf of X frx) =144x0.5 (y-0.5) dy =144(x-0.5)y-0.5) 3 1 =144(x-0.5)2x- 24 -12(x-0.5)similar for f(y)

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Step 3

In this case, X and Y are indep...

In this case
f(x. y) f()(y)
XYare independent
help_outline

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In this case f(x. y) f()(y) XYare independent

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