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>0.5 | Y=0.3). (a) Select the correct choice below and fill in the answer box to complete your choice. OA. O B. O C. O D. Since f(xly) = Since f(xly) = Since f(xly) = Since f(xly) = f(x,y) h(y) f(x,y) h(y) f(x,y) h(y) f(x,y) h(y) = = C... = , for 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>0.5 | Y=0.3).
(a) Select the correct choice below and fill in the answer box to complete your choice.
O A.
O B.
O C.
O D.
Since f(xly) =
Since f(xly) =
Since f(xly) =
Since f(xly) =
f(x,y)
h(y)
f(x,y)
h(y)
f(x,y)
h(y)
f(x,y)
h(y)
=
for 0<x< 1-y, involves the variable y, X and Y are not independent.
for 0<x< 1-y, is constant, X and Y are not independent.
for 0 <y <1-x, involves the variable x, X and Y are not independent.
for 0<x<1-y, is a function of only the variable x, X and Y are not independent.
f(x,y) =
12x², 0<x<1,0<y<1-x
0, elsewhere
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>0.5 | Y=0.3). (a) Select the correct choice below and fill in the answer box to complete your choice. O A. O B. O C. O D. Since f(xly) = Since f(xly) = Since f(xly) = Since f(xly) = f(x,y) h(y) f(x,y) h(y) f(x,y) h(y) f(x,y) h(y) = for 0<x< 1-y, involves the variable y, X and Y are not independent. for 0<x< 1-y, is constant, X and Y are not independent. for 0 <y <1-x, involves the variable x, X and Y are not independent. for 0<x<1-y, is a function of only the variable x, X and Y are not independent. f(x,y) = 12x², 0<x<1,0<y<1-x 0, elsewhere
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