Consider the following set of boolean variables about a randomly chosen day:

G : I was up late grading the night before

R : I get up feeling well-rested

S : it is a pleasant sunny day

H : I am feeling happy

O : people are sitting outside to have coffee

Draw a Bayes net that reasonably represents the relationships between those variables. (Hint: you are welcome to make assumptions such that your network is a polytree.)

Annotate the Bayes net with all necessary probabilities so that any possible question about the variables can be answered For the values, choose any reasonable number other than 0 or 1 (and don't just use the same value over and over!).

Compute the following probabilities based on your network. You may reuse any computations as needed.

P(r)

P(g ? s)

P(h) ["not h"]

P(r ? h)

P(s | o)