UNCERTAINTY

Question 1

can be represented as a number of events and the likelihood, or probability, of each of them happening.

Answer 1

Uncertainty

Question 2

Axioms in Probability

Answer 2

0 < P(ω) < 1: every value representing probability must range between 0 and 1.

The probabilities of every possible event, when summed together, are equal to 1.

Question 3

the degree of belief in a proposition in the absence of any other evidence.

Answer 3

Unconditional probability

Question 4

the degree of belief in a proposition given some evidence that has already been revealed

Answer 4

Conditional probability

Question 5

a variable in probability theory with a domain of possible values that it can take on

Answer 5

random variable

Question 6

is the knowledge that the occurrence of one event does not affect the probability of the other event.

Answer 6

independence

Question 7

P(a ∧ b) = P(a)P(b)

Answer 7

independence

Question 8

P(a | b)

Answer 8

conditional probability

Question 9

commonly used in probability theory to compute conditional probability

Answer 9

Bayes’ rule

Question 10

In words, Bayes’ rule says that the probability of b given a is equal to the probability of a given b, times the probability of b, divided by the probability of a.

Answer 10

Bayes’ rule

Question 11

the likelihood of multiple events all occurring

Answer 11

Joint probability

Question 12

Use to deduce conditional probability

Answer 12

joint probability

Question 13

P(¬a) = 1 - P(a)

Answer 13

negation

Question 14

P(a ∨ b) = P(a) + P(b) - P(a ∧ b)

Answer 14

Inclusion-Exclusion

Question 15

P(a) = P(a, b) + P(a, ¬b)

Answer 15

Marginalization

Question 16

P(a) = P(a | b)P(b) + P(a | ¬b)P(¬b)

Answer 16

Conditioning

Question 17

data structure that represents the dependencies among random variables.

Answer 17

bayesian network

Question 18

Bayesian networks have the following properties:

Answer 18

• They are directed graphs.
• Each node on the graph represent a random variable.
• An arrow from X to Y represents that X is a parent of Y. That is, the probability distribution of Y depends on the value of X.
• Each node X has probability distribution P(X | Parents(X)).

Question 19

Inference has multiple properties:

Answer 19

• Query X
• Evidence variables E
• Hidden variables Y
• The goal: calculate P(X | e)

Question 20

a process of finding the probability distribution of variable X given observed evidence e and some hidden variables Y.

Answer 20

inference by enumeration

Question 21

one technique of approximate inference

Answer 21

sampling

Question 22

each variable is sampled for a value according to its probability distribution

Answer 22

sampling

Question 23

likelihood weighting steps:

Answer 23

• Start by fixing the values for evidence variables.
• Sample the non-evidence variables using conditional probabilities in the Bayesian network.
• Weight each sample by its likelihood: the probability of all the evidence occurring.

Question 24

the probability of all the evidence occurring.

Answer 24

likelihood

Question 25

an assumption that the current state depends on only a finite fixed number of previous states.

Answer 25

markov assumption

Question 26

a sequence of random variables where the distribution of each variable follows the Markov assumption.

Answer 26

markov chain

Question 27

To start constructing a Markov chain, we need a _____ ______ that will specify the the probability distributions of the next event based on the possible values of the current event.

Answer 27

transition model

Question 28

a type of a Markov model for a system with hidden states that generate some observed event.

Answer 28

hidden markov model

Question 29

assumption that the evidence variable depends only on the corresponding state

Answer 29

sensor markov assumption

Question 30

Based on hidden Markov models, multiple tasks can be achieved:

Answer 30

- Filtering: given observations from start until now, calculate the probability distribution for the current state. For example, given information on when people bring umbrellas form the start of time until today, we generate a probability distribution for whether it is raining today or not. - Prediction: given observations from start until now, calculate the probability distribution for a future state. - Smoothing: given observations from start until now, calculate the probability distribution for a past state. For example, calculating the probability of rain yesterday given that people brought umbrellas today. - Most likely explanation: given observations from start until now, calculate most likely sequence of events.

Question 31

Consider a standard 52-card deck of cards with 13 card values (Ace, King, Queen, Jack, and 2-10) in each of the four suits (clubs, diamonds, hearts, spades). If a card is drawn at random, what is the probability that it is a spade or a two?

Answer 31

About 0.308

Question 32

Imagine flipping two fair coins, where each coin has a Heads side and a Tails side, with Heads coming up 50% of the time and Tails coming up 50% of the time. What is probability that after flipping those two coins, one of them lands heads and the other lands tails?

Answer 32

0.5 = 1/2

Question 33

Which of the following sentences is true? Assuming we know the train is on time, whether or not there is rain affects the probability that the appointment is attended. Assuming we know there is rain, whether or not there is track maintenance does not affect the probability that the train is on time. Assuming we know there is track maintenance, whether or not there is rain does not affect the probability that the train is on time. Assuming we know the train is on time, whether or not there is track maintenance does not affect the probability that the appointment is attended. Assuming we know there is track maintenance, whether or not there is rain does not affect the probability that the appointment is attended.

Answer 33

Assuming we know the train is on time, whether or not there is track maintenance does not affect the probability that the appointment is attended.

Question 34

Two factories — Factory A and Factory B — design batteries to be used in mobile phones. Factory A produces 60% of all batteries, and Factory B produces the other 40%. 2% of Factory A’s batteries have defects, and 4% of Factory B’s batteries have defects. What is the probability that a battery is both made by Factory A and defective?

Answer 34

0.012