Let A, B, C = {0, 1} be three binary random variables with the following joint...

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Let A, B, C = {0, 1} be three binary random variables with the following joint probability distribution: ABC P(A, B, C) 0 0 0 0.192 001 0.144 1 1 100 1 0 1 1 1 0 1 1 1 0 0 0 1 0.048 0.216 0.192 0.064 0.048 0.096 a) By direct calculation, compute the marginal P(A, B). b) By direct calculation compute the marginals P(A) and P(B). c) Are the random variables A and B dependent? Why or why not? d) Compute the conditional P(A, B | C) e) Show that A and B are conditionally independent, given C. Let A, B, C = {0, 1} be three binary random variables with the following joint probability distribution: ABC P(A, B, C) 0 0 0 0.192 001 0.144 1 1 100 1 0 1 1 1 0 1 1 1 0 0 0 1 0.048 0.216 0.192 0.064 0.048 0.096 a) By direct calculation, compute the marginal P(A, B). b) By direct calculation compute the marginals P(A) and P(B). c) Are the random variables A and B dependent? Why or why not? d) Compute the conditional P(A, B | C) e) Show that A and B are conditionally independent, given C.

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a A B PAB 0 0 0336 0 1 0192 1 0 0192 1 1 0096 The marginal PA B is the sum of all joint probabilitie... View the full answer