a) Suppose X, Y and Z are binary rv’s, each taking on the value 0 with probability 1/2 and the value 1 with probability 1/2. Find a simple example in which X, Y , Z are statistically dependent but are...

a) Suppose X, Y and Z are binary rv’s, each taking on the value 0 with probability 1/2 and the value 1 with probability 1/2. Find a simple example in which X, Y , Z are statistically dependent but are pairwise statistically independent (i.e., X, Y are statistically independent, X, Z are statistically independent, and Y , Z are statistically independent). Give pXY Z(x, y, z) for your example.

b) Is pairwise statistical independence enough to ensure that