C1: Probability Theory

Question 1

Population

Answer 1

A collection of all items under investigation.

Question 2

Parameter

Answer 2

A numerical description of some characteristic of the population.

Question 3

Experiment

Answer 3

A process whereby measurements are taken/observations are made to generate outcomes.

Question 4

Statistics

Answer 4

The scientific application of mathematical principles to the collection, analysis & presentation of numerical data.

Question 5

Types Of Experiments(2)

Answer 5

[A] Deterministic = a procedure whose outcome is certain.

[B] Random = a procedure whose outcome is uncertain.

Question 6

Outcome

Answer 6

Any observable phenomenon.

Question 7

Sample space/Event space (S)

Answer 7

= The collection of all possible outcomes of an experiment.

• represented by a Venn diagram.

Question 8

Event(E)

Answer 8

= a collection of outcomes from an experiment.
• denoted by a capital letter.
• the subset of a sample space.

Question 9

Types Of Events(2)

Answer 9

[A] Simple event/Elementary event = an individual outcome of an experiment.

[B] Null event = an event that contains no outcomes.
• represented by {} or crossed circle.

Question 10

Intersection (n)

Answer 10

= an overlap btwn events A and B.

• indicates common elements existing to both A and B.

Question 11

Union (U)

Answer 11

= occurs when similar outcomes are in both event A and B.

• combine.

Question 12

Complement of an event (E bar/ E’ / E to the c)

Answer 12

= occurs if event E doesn’t occur.

• has outcomes other than those of E but, they are in the sample space.

Question 13

Disjoint/Mutually exclusive

Answer 13

= occurs when events have nothing in common.

• empty intersection.

Question 14

Exhaustive

Answer 14

= when the union of events gives allnpossible outcomes for the experiment.
• A U E = S.

Question 15

Partition

Answer 15

= when events are mutually exclusive & collectively exhaustive.
• disjoint + exhaustive.

Question 16

Commutative Law

Answer 16

A U B = B U A

Question 17

Associative Law

Answer 17

A U (B U C) = (A U B) U C

Question 18

Distributive Law

Answer 18

A n (B U C) = (A n B) U (A n C)

Question 19

Idempotent Law

Answer 19

A U A = A

Question 20

De Morgan’s Laws

Answer 20

• (A U B)’ = A’ n B’

* (A n B)’ = A’ U B’

Question 21

Probability [P(•)]

Answer 21

= measure of uncertainty.
• common sense reduced to calculation.
• enables statisticians to use information in a sample to make inferences about the popn from which the same was obtained.

Question 22

Probability Axioms

Answer 22

= a function that to every event (E) assigns a non-native real no. P(E).

Question 23

Function

Answer 23

= a rule that assigns a real no. to each element of a set of objects (domain of function).

Question 24

Axiom I

Answer 24

0 < P(A) < 1

= probability of an event exists & is between zero and one.

Question 25

Axiom II

Answer 25

P(S) = 1.

• Y? –> because there is certainty of occurrence in a same space.

Question 26

Axiom III

Answer 26

● P (A U B) = P(A) + P(B)
- if A and B are disjoint events.

● P (A U B) = P(A) + P(B) - P(A n B)
- if A n B exists.