a)
Marginal distribution for X:
P(x = -1) = 1/3
P(x = 0) = 1/3
P(x = 1) = 1/3
Marginal distribution for Y:
P(y = 0) = 1/3 + 1/3 = 2/3
P(y = 1) = 1/3
We have:
E(X) = (-1)*(1/3) + 0*1/3 + (1)*(1/3) = 0
E(Y) = 0*(2/3) + 1*(1/3) = 1/3
and
E(XY) = (-1)*(0)*(1/3) + (0)*(1)*(1/3) + (1)*(0)*(1/3) = 0 + 0 + 0 = 0
Therefore E(XY) = E(X)E(Y) and as a result
X and Y are independent.
b)
cov(X,Y) = E(XY) - E(X)E(Y) = 0 - 0*(1/3) = 0 - 0 = 0
#cov(X,Y)=0
Suppose X and Y have joint distribution function given by: p(x, y) = for (x, y)...
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