10. Suppose Boolean parameterized random variables young(Person) and cool(Item) are parents of Boolean buys(Person, Item). Suppose there are 3000 people and 200 items.

(a) Draw this in plate notation.

(b) How many random variables are in the grounding of this model?

(c) How many numbers need to be specified for a tabular representation of this model.

(Do not include any numbers that are functions of other specified numbers.)

(d) Draw the grounding belief network assuming the population of Person is

{sam, chris} and the population of Item is {iwatch, mortgage, spinach}.

(e) What could be observed to make cool(iwatch) and cool(mortgage) probabilistically dependent on each other given the observations?