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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

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

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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
Transcribed Image Text: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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