the Domains are defined as dom(X)= {x, x'} designates for X=M,G,F,H.
I have computed the marginal distributions of the values to be as below: P(G=g) = 2000 P(M=m) = 1000 P(F=f) = 2800 P(H=h) = 4000
I am stuck at showing M and G are marginally independent but conditionally dependent given F. How is this done?
I have computed the marginal distributions of the values to be as below: P(G=g) = 2000 P(M=m) = 1000 P(F=f) = 2800 P(H=h) = 4000
Probability measures must lie betwixt $0$ and $1$ (inclusive). These do not.
Hint: Divide by the size of the sample space.
I am stuck at showing M and G are marginally independent but conditionally dependent given F. How is this done?
Recall the definition of independence. Two variables are independent if their joint probability is always equal to the product of their marginal probabilities.
1) Show $\mathsf P(M{=}m, G{=}g)=\mathsf P(M{=}m)~\mathsf P(G{=}g)$
2) Show $\mathsf P(M{=}m, G=g\mid F{=}f)\neq\mathsf P(M{=}m\mid F{=}f)~\mathsf P(G{=}g\mid F{=}f)$