Samples for Quiz 4

Task 1

Consider the given joint probabilty distribution for a domain of two variables (Color, Vehicle) :

	Color = Red	Color = Green	Color = Blue
Vehicle = Car	0.1184	0.1280	0.0736
Vehicle = Van	0.0444	0.0480	0.0276
Vehicle = Truck	0.1554	0.1680	0.0966
Vehicle = SUV	0.0518	0.0560	0.0322

Part a: Calculate P ( Color is not Green | Vehicle is Truck )

Part b: Check if Vehicle and Color are totally independant from each other

Task 2

In a certain probability problem, we have 11 variables: A, B₁, B₂, ..., B₁₀.

Variable A has 7 values.
Each of variables B₁, ..., B₁₀ have 8 possible values. Each B_i is conditionally indepedent of all other 9 B_jvariables (with j != i) given A.

Based on these facts:

Part a: How many numbers do you need to store in the joint distribution table of these 11 variables?

Part b: What is the most space-efficient way (in terms of how many numbers you need to store) representation for the joint probability distribution of these 11 variables? How many numbers do you need to store in your solution? Your answer should work with any variables satisfying the assumptions stated above.

Part c: Does this scenario follow the Naive-Bayes model?

Task 3

Part a (Solve before Part b)

George doesn't watch much TV in the evening, unless there is a baseball game on. When there is baseball on TV, George is very likely to watch. George has a cat that he feeds most evenings, although he forgets every now and then. He's much more likely to forget when he's watching TV. He's also very unlikely to feed the cat if he has run out of cat food (although sometimes he gives the cat some of his own food). Design a Bayesian network for modeling the relations between these four events:

baseball_game_on_TV
George_watches_TV
out_of_cat_food
George_feeds_cat

Your task is to connect these nodes with arrows pointing from causes to effects.

Part b (Solve after Part a)

You have been given the correct answer for Part A (here). You have also been given the conditional probabilties of each variable given it's parents. Calculate P ( not(Baseball Game on TV) | not(George Feeds Cat) ) using Inference by Enumeration

Task 4

Part a: On the network shown above, what is the Markovian blanket of node L?

Part b: On the network shown above, what is P(A, F)? How is it derived?

Part c: On the network shown above, what is P(M, not(C) | H)? How is it derived?

Note: You do not have to use Inference by Enumeration for parts b and c.