Let's say we have the following problem from this book:
Consider a very simple medical diagnosis setting, where we focus on two diseases — flu and hayfever; these are not mutually exclusive, as a patient can have either, both, or none. Thus, we might have two binary-valued random variables, Flu and Hayfever. We also have a 4-valued random variable Season, which is correlated both with flu and hayfever. We may also have two symptoms, Congestion and Muscle Pain, each of which is also binary-valued. Overall, our probability space has 2 × 2 × 4 × 2 × 2 = 64 values.
which describes the following independence rules: $$F\bot H|S$$ $$C\bot S|F,H$$ $$M\bot H,C|F$$ $$M\bot C|F$$
where the notation in general means:
$$A\bot B|C \Longleftrightarrow P(A \cap B|C)=P(A|C)P(B|C)\Longleftrightarrow P(A|B \cap C) = P(A|C) \Longleftrightarrow\ Given\ C, then\ A,B\ are\ conditionally\ independent$$
The first independence means that if we know the season, we don't need to know if the person has hayfever to diagnose if he has the flu.
So the book states that if we take into account these independencies then:
This parameterization is significantly more compact, requiring only 3+4+4+4+2 = 17 nonredundant parameters, as opposed to 64...
My question is why 17 nonredundant parameters? How did we reach to this result?