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> 0.2 | Y=0.6). (a) Select the correct choice below and fill in the answer box to complete your choice. OA. f(x,y) h(y) O B. 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) = f(x,y) h(y) 12x², 0
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> 0.2 | Y=0.6). (a) Select the correct choice below and fill in the answer box to complete your choice. OA. f(x,y) h(y) O B. 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) = f(x,y) h(y) 12x², 0
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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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>0.2 | Y=0.6).
(a) Select the correct choice below and fill in the answer box to complete your choice.
O A.
O B.
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, is constant, X and Y are not independent.
2
f(x, y) =
, for 0 <y<1-x, involves the variable x, X and Y are not independent.
3x
12x², 0<x<1, 0<x<1-x
0₁
elsewhere
(1-y)
for 0<x< 1-y, involves the variable y, X and Y are not independent.
3
(b) P(X>0.2 | Y=0.6) = 0.875000
(Simplify your answer. Round to six decimal places as needed.)
for 0<x<1-y, is a function of only the variable x, X and Y are not independent.
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