Probability in Data Science

Question 1

Probability Space

Answer 1

Consists of sample space, event space and probability

Question 2

Sample Space

Answer 2

Represented by the Greek letter omega, it represents all possible outcomes.

Question 3

Event Space

Answer 3

This represents every possible combination of elementary events.

Question 4

Three Axioms

Answer 4

1) P(A) always has to be positive.

Question 5

Mutually Exclusive

Answer 5

If the events can’t happen simultaneously.

Question 6

P(A u B)

Answer 6

If mutually exclusive/independent, P(A) + P(B) - P(A n B).

Question 7

P(A n B)

Answer 7

If independent, P(A) * P(B)
If dependent, P(A|B)/P(B) or P(B|A)/P(A)

Question 8

Mutual independence vs pairwise independence

Answer 8

If something is mutually independent it is also pairwise independent.
Pairwise independent tests the probability of pairs to see if they are independent with P(A n B) = P(A)P(B), whilst mutually independency tests all values to check that everything is independent together.

Question 9

How to partition sample space

Answer 9

Lets say we have an event A with a sample space B, and that A ⊆ B. If we were to divide B into multiple partitions, lets say {B_1, B_2, … , B_5}, we can use these to figure out the probability of A. This is done by:
P(A) =
Σ_n P(A and B_n) =
ΣP(A|B_n)P(B_n).

Question 10

Bayes Theorem

Answer 10

P(A | B) = P(B | A) x P(A) / P(B)
We could rewrite P(B) as:
P(B | A) x P(A) + P(B | ¬A) x P(¬A)

Question 11

Bayesian Network

Answer 11

A probabilistic graphical model that represents a set of variables and their conditional dependencies via a Directed Acyclic Graph.

Question 12

Base Rate Fallacy

Answer 12

P(A | B) != P(B | A)