The joint probability distribution is x 1 0 0 1 y 0 1 1 0 fXY (x, y) Show that the correlation between X and Y is zero, but X and Y are not independent

Question: The joint probability distribution is x - 1 0 0 1 y 0 -1 1 0 fXY (x, y) Show that

The joint probability is
x - 1 0 0 1
y 0 -1 1 0
fXY (x, y) ¼ ¼ ¼ ¼
Show that the correlation between X and Y is zero, but X and Y are not independent.

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