Uncertainty

Question 1

Sensor Uncertainty

Answer 1

Not being able to perfectly identify current state

Question 2

Probabilistic Interence

Answer 2

• Represent components of state as random variables.
• Random variables can be discrete or continuous.
• Sampling by observing many times

Question 3

Discrete Random Variable

Answer 3

Can only have two values

Question 4

Continuous Random Variable

Answer 4

Can have a range of different values

Question 5

Rules of Probability

Answer 5

1. Probability that RV takes on some value is always between 1 and 0 ( 0 <= p(x=x) <= 1 )
2. Probability of deterministic events ( p(true) = 1, p(false) = 0 )
3. Additivity ( p(a | b) = p(a) = p(b) - p(a & b) )

Question 6

Joint Distribution

Answer 6

Probability distribution that includes multiple interacting RVs

Question 7

Event

Answer 7

Setting of some subset of random variables

Question 8

Marginalization

Answer 8

Using joint distribution to compute probability of any event by adding up all table entries corresponding with the given configuration.

Question 9

Conditional Probability

Answer 9

When one RV impacts the value of another.
( p(y=w | x=v) = ( p(y=w & x=v) / ( p(x=v) ) )

Question 10

Normalization

Answer 10

Don’t have to know/compute the denominator when calculating conditional prob.
( p(x|E=e) = p(x, E=e) / p(E=e) = alpha * p(x, E=e) )

Question 11

Hidden Variables

Answer 11

RV that doesn’t have a setting, added into calculations

Question 12

Conditioning

Answer 12

Can marginalize and leverage the definition of condition probability to access other conditional probabilities

Question 13

Independence

Answer 13

When the joint probability of two RVS is the same as the product of their marginals

Question 14

Bayes Rule

Answer 14

Additional true fact about conditional probabilities.
p(a|b) = ( p(b|a) * p(a) 0 / p(b)

p(b|a) * p(a) = p(a, b) = p(a|b) * p(b)

Question 15

Product Rule

Answer 15

p(a, b, c) = p(a, b | c) * p(c) = p(a\b, c) * p(b|c) * p(b)