Probability

Question 1

What is a sample space?

Answer 1

A sample space is a set of point, they are the possible outcomes of a trial.

Question 2

What is an event

Answer 2

An event is a subset of a sample space

Question 3

What is a probability function

And its properties

Answer 3

A probability is a map from events to real numbers such that
1. P(A) ≥ 0 for all events.
2. P(X) = 1
3. If A ∩ B = ∅ for two events A and B then
P(A ∪ B) = P(A) + P(B)

Question 4

What is a probability mass function

And its properties

Answer 4

A probability mass function is a map from points in the sample space to real numbers
such that

Question 5

How does a probability function relate to a probability mass function?

Answer 5

Question 6

Calculate the probability of event A given all points in sample space have the same probability.

Answer 6

Question 7

What is the binomial coefficient

Answer 7

Question 8

What is the partitian function

Answer 8

Question 9

What is conditional probability (and formula)

Answer 9

Question 10

What is independence (formula)

Answer 10

Question 11

What is conditional independence (formula)

Answer 11

Question 12

What is Bayes’ rule (formula)

Answer 12

Question 13

How does a naïve Bayes estimator work

Answer 13

Question 14

What is a random variable

Answer 14

A random variable is a map from sample space to a set of numerical values

Question 15

How to calculate P(X=x)

Answer 15

Question 16

What is a probability distribution

Answer 16

A probability distribution is a table of probabilities for a random variable.

Question 17

What are joint, conditional and marginal distributions?

Answer 17

Question 18

How to calculate the expected value of a function

Answer 18

Question 19

What is the mean

Answer 19

Question 20

What is the varience

Answer 20

Question 21

What is the nth moment

Answer 21

Question 22

Properties of expected values (multiplication, addition, identity)

Answer 22

Question 23

How to calculate varience using the 2nd moment and square of mean

Answer 23

Question 24

What determines an event to be part of the Poisson process?

Answer 24

Question 25

What is the Poisson distribution (and formula)

Answer 25

Question 26

What is the distribution function

Answer 26

Question 27

What is the density function (in relation to distribution function)

Answer 27

Question 28

Determine distribution function from density function

Answer 28

Question 29

Determine distribution function between 2 values

Answer 29

Question 30

What does the Gauss/Normal distribution look like?

Answer 30

Question 31

What is the density function for the Gauss Distribution

Answer 31

Question 32

How to work out pobabilities of the Gauss distribution

Answer 32

Question 33

Sum of a geometric series (and infinite) formula

Answer 33

Question 34

Binomial distribution formula

Answer 34

Question 35

Mean and varience of binomial distribution

Answer 35

Mean: np
Varience np(1-p) or npq

Question 36

How to derive mean and varience of binomial distribution

Answer 36