$(20$ pts $)$ Given the below influence diagram that all Decisions and Risks are binary $($have only two states, e$.$g$.,$ black$/$white$,$ up$/$down$,$ hot$/$cold$)$

a$.$ Of the five connecting arrows, how many could show relevance not merely timing? Why?

b$.$ Can there be more than one correct representation of the decision tree corresponding to this influence diagram? If no$,$ why not. If yes, about how many different "correct" trees are there?

c$.$ What does the arrow between Risk $1$ and Risk $2$ signify?

d$.$ Is Outcome a function of Risk $1,$ Risk $2$ and Decision $2$ or just Risk $2$ and Decision $2?$ Why?

e$.$ Convert this influence diagram to a decision tree