8 - Fundamentals of Probability

Question 1

What is Intrinsically random behavior?

Answer 1

Making decisions under uncertainty

Question 2

What is Utility theory?

Answer 2

It is used to represent and infer preferences

Question 3

What are Random Variables?

Answer 3

a function from the sample space of an experiment to the set of real numbers. That is, a random variable assigns a real number to each possible outcome - We describe the (uncertain) state of the world using random variables

A random variable is a function. It is not a variable, and it is not random!

Question 4

What is an Atomic event?

Answer 4

a complete specification of the state of the world, or a complete assignment of domain values to all random variables * Atomic events are mutually exclusive and exhaustive

Question 5

What are Joint probability distributions?

Answer 5

A joint distribution is an assignment of probabilities to every possible atomic event

Question 6

What are Marginal probability distributions?

Answer 6

Suppose we have the joint distribution P(X,Y)and we want to find the marginal distribution P(X) - General rule: to find P(X = x), sum the probabilities of all atomic events where X = x

Question 7

What is Conditional probability?

Answer 7

A conditional distribution is a distribution over the values of one variable given fixed values of other variables

Question 8

What is Probabilistic inference?

Answer 8

the agent observes the values of some random variables X1, X2, …, Xnand needs to reason about the values of some other unobservedrandom variables Y1, Y2, …, Ym