Question: 5. (25 points) Consider the uniform joint pdf over the following domain of x1 and X2. Domain [fx1,X2 (21, 22)] = 2 = 1- x1

5. (25 points) Consider the uniform joint pdf over the following domain of x1 and X2. Domain [fx1,X2 (21, 22)] = 2 =

5. (25 points) Consider the uniform joint pdf over the following domain of x1 and X2. Domain [fx1,X2 (21, 22)] = 2 = 1- x1 if x1 e [0, 1] 22 = 1 +1 if x e [-1,0] 0.9 0.8 0.7 0.6 cy 0.5 0.4 0.3 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 0.5 0.8 0.5 0.2 -0.5 (a) (7 points) If X1 and X2 are orthogonal as defined above are they also uncorrelated? Provide clear reasoning. (b) (6 points) Are X1 and X2 independent? Provide clear reasoning.

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