## CMSC 471 Artificial Intelligence Pretest

Name: _____________________________________

Disclaimer: Please do not worry if you cannot answer a question on this pretest. I don't want this to be a concern for people. Just do your best, and do it without pulling out textbooks or hair.

1.) What is your year and major(s)/minor(s)?    e.g. senior CMSC major

2.) Which of the following courses have you taken and passed?

CMSC 341 ___     MATH 221 _____     STAT 355 _____    STAT 451 _____

3.) Are you on the CS game development track?    Are you interested in it?

4.) Are you also registered for CMSC 491M (Machine Learning) this semester?

Yes ___     No _____

5.) What are you most excited about in this class?

6.) What are you most concerned about regarding this class?

7.) Express the following English sentence in first-order logic using quantifiers, without using the uniqueness quantifier (∃!).

Mary has exactly two favorite toys of those she owns.

Let Fav(p, x) be the predicate that x is a favorite of pOwns(p, x) be the predicate that p owns xToy(x) be the predicate that x is a toy, and let the universe of discourse be all objects and people in the world.

8.) Define the following terms:

• Degree of a graph:
• Branching factor of a tree:
• Depth of a tree:

9.) For this problem, consider the binary random variables X, Y, and Z with the following distribution:
 ~X X ~Y Y ~Y Y ~Z 0 0.125 0.125 0 Z 0.25 0.25 0 0.25

• What is the joint distribution of Y and Z?
• What are the marginal distributions of Y and Z?
• What is the conditional distribution of X given ~Z?
• Are X and Z independent?
• Are X and Y independent?

10.) On the following axis, sketch the plot of the probability density function of a one-dimensional Gaussian random variable x with mean m > 0 and variance s. Label the graph, and specifically those values.

• Give the mathematical expression for this pdf (without looking it up).