Question

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 > 0.1 | Y = 0.4). f(x,y) = { 20x^3, 0 < x < 1, 0 < y < 1 - x; 0, elsewhere (a) Select the correct choice below and fill in the answer box to complete your choice. A. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, is a function of only the variable x, X and Y are not independent. B. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, involves the variable y, X and Y are not independent. C. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < y < 1 - x, involves the variable x, X and Y are not independent. D. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, is constant, X and Y are not independent.

          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 > 0.1 | Y = 0.4).
f(x,y) = { 20x^3, 0 < x < 1, 0 < y < 1 - x; 0, elsewhere
(a) Select the correct choice below and fill in the answer box to complete your choice.
A. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, is a function of only the variable x, X and Y are not independent.
B. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, involves the variable y, X and Y are not independent.
C. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < y < 1 - x, involves the variable x, X and Y are not independent.
D. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, is constant, X and Y are not independent.

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 > 0.1 | Y = 0.4).
f(x,y) = 20x^3, 0 < x < 1, 0 < y < 1 - x; 0, elsewhere
(a) Select the correct choice below and fill in the answer box to complete your choice.
A. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, is a function of only the variable x, X and Y are not independent.
B. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, involves the variable y, X and Y are not independent.
C. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < y < 1 - x, involves the variable x, X and Y are not independent.
D. Since f(x|y) = f(x,y) / h(y) = [ ], for 0 < x < 1 - y, is constant, X and Y are not independent.

Added by Fernando H.

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