Lab Assignment 1 Environments Search Bayes Nets

Problem 1: Peg Solitaire Is Peg Solitaire: Partially observable? Stochastic? Continuous? Adversarial? Play online at:

Problem 2: Loaded Coin Is Loaded Coin: Partially observable? Stochastic? Continuous? Adversarial? The coin above might be fair (0.5 chance of heads, 0.5 chance of tails), or it might be loaded (p chance of heads, 1-p chance of tails, p != 0.5). The Loaded Coin problem is to determine whether the coin is fair or loaded. You don’t need to solve Loaded Coin, but answer the questions on the right.

Problem 3: Maze Traversal Is Maze Traversal: Partially observable? Stochastic? Continuous? Adversarial? O X start goal Maze Traversal: get from the start position to the goal position. Answer the questions about the maze traversal problem on the right.

Problem 4: Search Tree Counting the start node and goal node, how many nodes are expanded if we go 1.Left-to-right a.Breadth-first: b.Depth-first: 2.Right-to-left a.Breadth-first: b.Depth-first: start goal

Problem 5: Search Network Counting the start node and goal node, how many nodes are expanded if we go 1.Left-to-right a.Breadth-first: b.Depth-first: 2.Right-to-left a.Breadth-first: b.Depth-first: start goal

Problem 6: A* Search A B C D start goal The table above shows the state space for a search problem: grid elements A1 through D6. The values in each cell indicate the value of a heuristic function h(x) for that cell grid. 1.Is the heuristic function admissible? 2.Which node will be expanded first: A2 or B1? 3.Which node will be expanded second: B1, C1, A2, A3, or B2? 4.Which node will be expanded third: D1, C2, B3, or A4?

Problem 7: Bayes Rule Assume the following are true regarding binary random variables A and B: P(A) = 0.5 P(B | A) = 0.2 P(B |  A) = 0.8 What is P(A | B)?

Problem 8: Simple Bayes Net P(A) = 0.5  i P(X i | A) = 0.2  i P(X i |  A) = What is P(A | X 1 X 2  X 3 )? 2. What is P(X 3 | X 1 )? A X1X1 X2X2 X3X3

Problem 9: Conditional Independence B  C? B  C | D? B  C | A? B  C | A, D? A BC D

Problem 10: Conditional Independence 2 C  E | A? B  D | C, E? A  C | E? A  C | B? A BD E C

Problem 11: Parameter Counting How many parameters are needed to specify a full joint distribution over 5 binary variables? For the Bayes Net on the left, assuming all 5 variables are binary, how many parameters are needed? A BD E C