The joint density function of the random variables X and Y is given to the right. (a) Show that X and Y are not independent. (b) Find P(X> 0.3 Y = 1.3). 3 f(x,y) = { 4X, 0

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The joint density function of the random variables X and Y is given to the right.
(a) Show that X and Y are not independent.
(b) Find P(X> 0.3 Y= 1.3).
3
f(x,y) = { 4X, 0<x<2, 0<y<2-x
0,
elsewhere
(a) Select the correct choice below and fill in the answer box to complete your choice.
O A.
f(x,y)
Since f(x|y) =
h(y)
for 0<x<2- y, is a function of only the variable x, X and Y are not independent.
%3D
OB.
f(x,y)
Since f(xly) =
h(y)
for 0 <x<2- y, is constant, X and Y are not independent.
%3D
Oc.
f(x,y)
Since f(xly) =
h(y)
for 0 <y<2-x, involves the variable x, X and Y are not independent.
OD.
f(x,y)
Since f(xly) =
h(y)
for 0<x<2- y, involves the variable y, X and Y are not independent.
Transcribed Image Text:The joint density function of the random variables X and Y is given to the right. (a) Show that X and Y are not independent. (b) Find P(X> 0.3 Y= 1.3). 3 f(x,y) = { 4X, 0<x<2, 0<y<2-x 0, elsewhere (a) Select the correct choice below and fill in the answer box to complete your choice. O A. f(x,y) Since f(x|y) = h(y) for 0<x<2- y, is a function of only the variable x, X and Y are not independent. %3D OB. f(x,y) Since f(xly) = h(y) for 0 <x<2- y, is constant, X and Y are not independent. %3D Oc. f(x,y) Since f(xly) = h(y) for 0 <y<2-x, involves the variable x, X and Y are not independent. OD. f(x,y) Since f(xly) = h(y) for 0<x<2- y, involves the variable y, X and Y are not independent.
Expert Solution
Step 1:-

To find if X and Y are independent or not,

 Calculate marginal density function of y, h(y) 

If f(X/y) is constant then X and y are independent otherwise these variables are dependent. 

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