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Actuarial Technician L4 > Chapter 1 Notation & terminology > Flashcards

Chapter 1 Notation & terminology Flashcards

1
Q

1.1 Sets

What is a set?

A

A set is a collection of objects.

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2
Q

1.1 Sets

What is an element?

element of a set?

A

Each object in a set is said to be an element of the set.

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3
Q

1.1 Sets

What do round brackets and square brackets indicate in a set?

for example [0,10)

A

A round bracket indicases that the endpoint is not included in the set.
A square bracket indicates that the endpoint is included in the set.

[0,10) is the set of values that 0 0,10) is the set of values of x such

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4
Q

1.1 Sets

What does ∅ mean?

A

The empty set, ie. the set that contains no elements

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5
Q

1.1 Sets

What does ∈ mean?

A

Is a member of the set

if S is the set of even numbers, then 2∈S

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6
Q

1.1 Sets

What does ∉ mean?

A

Is not a member of the set

if S is the set of even numbers, then 13∉S

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7
Q

1.1 Sets

What does ⊂ mean?

A

Is a subset of

C⊂D if every element of the set C is also an element of the set D

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8
Q

1.1 Sets

What does ⊄ mean?

A

Is not a subset of

C⊄D means that the set C contains at least one element that is not an el

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9
Q

1.1 Sets

What does ∪ mean?

A

Union (Or)

C∪D is the set of elements contained in set C or set D or both

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10
Q

1.1 Sets

What does ∩ mean?

A

Intersection (And)

C ∩ D is the set of elements in set C that are also elements of set D

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11
Q

1.1 Sets

What does Ā mean?

A

Complement of set A

Ā is the set of elements that do not belong to set A

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12
Q

1.1 Sets

What does A’ mean?

A

Alternative notation for the complement of set A

complement being the set of elements that do not belong to set A

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13
Q

1.1 Sets

What does ℕ mean?

A

The set of natural numbers

ℕ = {1,2,3,4,…]

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14
Q

1.1 Sets

Should 0 be included in ℕ?

A

We use the convention that 0 is not a member of this set

Some mathematicians do define the set of natural number to include 0

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15
Q

1.1 Sets

What does ℤ mean?

A

The set of intergers

ℤ = {…,-3,-2,-1,0,1,2,3,…}

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16
Q

1.1 Sets

What does ℚ mean?

A

The set of rational number (fractions)

the set numbers of the form p/q, where p,q ∈ ℤ and q ≠ 0

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17
Q

1.1 Sets

What does ℝ mean?

A

The set of real numbers

the set of all number between - ∞ and ∞

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18
Q

1.1 Sets

What does the superscripts + or - mean in situations such as ℤ+ or ℤ-

In the example the + and - should be superscript

A

the + or - refers to the positive or negative numbers
with in the set respectivally

ℤ = {…,-3,-2,-1,0} = ℕ

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19
Q

1.2 Logic & Proofs

What does ∀ mean?

A

For all

(Xsquared) 1> ∀>x 1

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20
Q

1.2 Logic & Proofs

What does ∃ mean?

A

There exists

∃ x ∈ ℝ such that x+1= 5

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21
Q

1.2 Logic & Proofs

What does ∄ mean?

A

There does not exist

∄ x ∈ ℕ such that xsquared = 2

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22
Q

1.2 Logic & Proofs

What does : mean?

A

Such that

ℝ−= {x : - ∞< X<0}

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23
Q

1.2 Logic & Proofs

What does st mean?

A

Such that

∃x∈ ℝ st x + 1 = 5

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24
Q

1.2 Logic & Proofs

What does ⇒ mean?

A

Implies

x = -2 ⇒ xsquared = 4

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25
Q

1.2 Logic & Proofs

What does ⇐⇒ mean?

A

Implies and is implied by (equlivent to)

X = 0 ⇐⇒ xcubed = 0

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26
Q

1.2 Logic & Proofs

What does iff mean?

A

If and only if (same meaning as ⇐⇒)

n is even iff n/2 ∈ℤ

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27
Q

1.2 Logic & Proofs

What does → mean?

A

Tends to (or approaches)

1/x → 0 as x → ∞

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28
Q

1.2 Logic & Proofs

What does the superscript + mean in situations such as
x→1+

the + in the example should be superscript

A

X is approaching 1 from above - but is always slightly greater than 1

1/x → 0+ as x → ∞

Writting x → 1 without a super script + or - means x is approaching 1 from either direction

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29
Q

1.2 Logic & Proofs

What does the superscript - mean in situations such as
x→1-

the - in the example should be superscript

A

X is approaching 1 from below - is always slightly less than 1

1/x → 0- as x → -∞

Writting x → 1 without a super script + or - means x is approaching 1 from either direction

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30
Q

1.2 Logic & Proofs

How do we define Necessary?

A

If A is necessary for B,
then B ⇒ A,
B is true only if A is true

A = the number x is divisable by 5, B = the integer x ends in 5

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31
Q

1.2 Logic & Proofs

How do we define Sufficient?

A

If A is sufficient for B,
then A ⇒ B,
B is true if A is true

A = the integer x ends in 5, B = the number x is divisable by 5

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32
Q

1.2 Logic & Proofs

How do we define Necessary & Sufficient?

A

If A is necessary and sufficient for B,
then A ⇐⇒ B,
A and B are equlivent statments

A = the interger x is divisible by 2, B = the number x is even

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33
Q

1.3 Mathematical Constants

What is the mathmatical constant e?

Eulers Number

A

e is the natural language of growth
On a graph e to the power of x at any point has the same value, gradient & area under the curve

eg. interest on £1 every moment (1+1/n) to power of n → e as n → ∞

The value of e is: 2.718281828…

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34
Q

1.4 Greek letters

What does the greek letter α mean, and how is it most often used?

A

alpha = parameter

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35
Q

1.4 Greek letters

What does the greek letter β mean, and how is it most often used?

A

lower case beta = parameter

or upper case = B = beta function

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36
Q

1.4 Greek letters

What does the greek letter B mean, and how is it most often used?

A

upper case beta = beta function

or lower case = β = parameter

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37
Q

1.4 Greek letters

What does the greek letter γ mean, and how is it most often used?

A

lower case gamma = parameter

or upper case = Γ = gamma function

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38
Q

1.4 Greek letters

What does the greek letter Γ mean, and how is it most often used?

A

upper case gamma = gamma function

or lower case = γ = parameter

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39
Q

1.4 Greek letters

What does the greek letter δ mean, and how is it most often used?

A

lower case delta = small change

or upper case = Δ = difference

40
Q

1.4 Greek letters

What does the greek letter Δ mean, and how is it most often used?

A

upper case delta = difference

or lower case = δ = small change

41
Q

1.4 Greek letters

What does the greek letter ε mean, and how is it most often used?

A

epsilon = small quantity

42
Q

1.4 Greek letters

What does the greek letter θ mean, and how is it most often used?

A

theta = parameter

43
Q

1.4 Greek letters

What does the greek letter κ mean, and how is it most often used?

A

kappa = parameter

44
Q

1.4 Greek letters

What does the greek letter λ mean, and how is it most often used?

A

lambda = parameter

45
Q

1.4 Greek letters

What does the greek letter μ mean, and how is it most often used?

A

mu = mean, mortality rate

46
Q

1.4 Greek letters

What does the greek letter ν mean, and how is it most often used?

A

nu = mortality rate when sick

47
Q

1.4 Greek letters

What does the greek letter π mean, and how is it most often used?

A

lower case pi = 3.14

or upper case = Π = product

48
Q

1.4 Greek letters

What does the greek letter Π mean, and how is it most often used?

A

upper case pi = product

or lower case = π = 3.14

49
Q

1.4 Greek letters

What does the greek letter ρ mean, and how is it most often used?

A

rho = correlation coefficient, recovery rate

50
Q

1.4 Greek letters

What does the greek letter σ mean, and how is it most often used?

A

lower case sigma = standard deviation, sickness rate

or upper case = Σ = sum

51
Q

1.4 Greek letters

What does the greek letter Σ mean, and how is it most often used?

A

upper case sigma = sum

or lower case = σ = standard deviation, sickness rate

52
Q

1.4 Greek letters

What does the greek letter τ mean, and how is it most often used?

A

tau = parameter

pronounced as in first syllable of tower (sometimes pronounced tall)

53
Q

1.4 Greek letters

What does the greek letter φ mean, and how is it most often used?

A

lower case phi = probability density function of standard normal distrobution

upper case = Φ

54
Q

1.4 Greek letters

What does the greek letter Φ mean, and how is it most often used?

A

upper case phi = cumulative distribution function of standard normal distribution

lower case = φ

55
Q

1.4 Greek letters

What does the greek letter χ (χ²) mean, and how is it most often used?

A

chi =chi² = distribution

pronounced as first syllable of ‘Cairo’

56
Q

1.4 Greek letters

What does the greek letter ψ mean, and how is it most often used?

A

psi = probability of ultimate ruin

57
Q

1.4 Greek letters

What does the greek letter ω mean, and how is it most often used?

A

omega = limiting age in a life table

58
Q

1.5 Expressions, equations, formulae, terms & factors

How would you define an ‘Expression’?

A

A mathematical expression is any combination of mathematical symbols, eg:
2+2,
1.09²
x + 2y,
2(b-c)
Usually expressions involve more than one symbol and many expressions include letters.

May not contain the ‘equal to’ sign or any type of inequality.

59
Q

1.5 Expressions, equations, formulae, terms & factors

How would you define an ‘Equation’?

A

An equation is a statement concerning the equality of two expressions. Some examples of equations are given below:
2+2=4,
1.09² = 1.1881,
x+2y= -5
a(b-c)=ab-ac

In word processing packages the word ‘equation’ is often used more generally to mean anything containing mathematical symbols, which is not strictly correct

60
Q

1.5 Expressions, equations, formulae, terms & factors

How would you define ‘Formulae’?

A

A formula is a special type of equation that shows the relationship between different quantities. For example, the formula for area of a triangle is as follows:
area =1/2×base height

A formula often uses letters to represent the variables. circumference of a circle is:
C=2πR
In this formula, C denotes circumference and r denotes radius.

61
Q

1.5 Expressions, equations, formulae, terms & factors

How would you define Terms?

As in Terms, Factors, and Coefficients

A

A term is an element in an expression that is added or subtracted. For example, the terms in the expression ab-ac are ab and ac.

62
Q

1.5 Expressions, equations, formulae, terms & factors

How would you define Factros?

As in Terms, Factors, and Coefficients

A

A factor is an element in an expression that is multiplied or divided. For example, the factors in the expression a(b-c) are a and b-c.

63
Q

1.5 Expressions, equations, formulae, terms & factors

How would you define Coefficients?

As in Terms, Factors, and Coefficients

A

A numerical factor appearing in an expression, such as the 3 in 3x², is also called a coefficient.

64
Q

1.6 Dimensions and units of measurement

What is a ‘Dimension’?

A

Dimensions are used to show what a numerical value actually represents.
pounds, meters, years, kilograms

Numbers/coefficients (inc π & e ) have no dimension & are dimensionless.

65
Q

1.6 Dimensions and units of measurement

Can values with different dimensions be added or subtracted?

A

No, you can not add £2 and 5 years together. Where possable different units/dimensions need to be converted when adding, eg. £2 and $5 or 2m and 500cm

66
Q

1.6 Dimensions and units of measurement

What happens when two values with the same dimension are divided?

A

The resulting values will be dimensionless.

10 years / by 5 years is 2 (not 2 years)

67
Q

1.7 Conventions used in financial and actuarail mathematics

How would you commonaly write if the scientic notation (standard form) is: $6.2x10(po6)

A

£6.2m

68
Q

1.7 Conventions used in financial and actuarail mathematics

What is the importance of using ‘precentage points’ and ‘basis points’?

A

To clearly diferantiage between adding/subtracting precentages, not multiplying them.

6% increased by 2 precentage points is 8%
6% increased by 2 precent is 6*1.02=6.12%

Basis points are used to comunicate this as 100th of a precentage point.
6% increased by 125bps is 7.25%

69
Q

1.7 Conventions used in financial and actuarail mathematics

How are negative values shown in accounting?

A

In brackets
£(0.2m)
Is a negative of £200,000

70
Q

1.7 Conventions used in financial and actuarail mathematics

What does this Δ mean?

A

Δ is used to denote a change in quantity. eg.
Δ profit = £534K means profit has risen by £534,000.
Δ profit = £(534K) means profit has fallen by £534,000.

Upper case Delta

71
Q

1.8 Time Intervals

How are annual quaters defined?

A

Q1 = 1 Jan to 31 Mar
Q2 = 1 Apr to 30 Jun
Q3 = 1 Jul to 30 Sep
Q4 = 1 Oct to 31 Dec

Normally sufficiently accurate to assume a quarter is exactly 1/4 year

72
Q

1.8 Time Intervals

When is the tax year (fiscal year) in the UK?

A

6 April to 5 April

So, for example, the 2014/15 tax year is the period from 6 April 2014 to 5 April 2015 (both days inclusive).

Tax years differ between countries.

73
Q

1.8 Time Intervals

How is a year represented in actuarial notation?

A

using a right-anble symbol
5 years is represented by 5⌉

(but with the top of the box covering the top of the 5)

74
Q

1.9 Glossary

A Life

Basic actuarial terminology

A

Just means a person

75
Q

1.9 Glossary

A First-Class Life

Basic actuarial terminology

A

A person in perfect health

76
Q

1.9 Glossary

An Impaired Life

Basic actuarial terminology

A

A person NOT in perfect health

77
Q

1.9 Glossary

Immediate

Basic actuarial terminology

A

Within the next year
eg. an immediate pension would make the first payment at some time during the commingyear but not necessarily at the start of that year

Opposite of Deferred

78
Q

1.9 Glossary

Deferred

Basic actuarial terminology

A

In the future (not within the next year)
eg. a deferred pension would normally start making payments a number of years in the future

Opposite of Immediate

79
Q

1.9 Glossary

Level

Basic actuarial terminology

A

Constant
eg. level payments are for the same amount each time

80
Q

1.9 Glossary

Net Pay/Payment

Basic actuarial terminology

A

Where something has been deducted.
Net subs = sub - IPT
Net pay = salary - tax, controbutions, study loan

Ask - what has been deducted?

81
Q

1.9 Glossary

Gross Pay/Payment

Basic actuarial terminology

A

Total value without deductions.

Ask - does anything need to be deducted?

82
Q

1.9 Glossary

Life Office/Office

Basic actuarial terminology

A

Just means insurance company

83
Q

1.9 Glossary

Outgo

Basic actuarial terminology

A

amounts that are going out

opposite of income

84
Q

1.9 Glossary

Income

Basic actuarial terminology

A

amounts that are coming in

opposite of outgo

85
Q

1.9 Glossary

Payable

Basic actuarial terminology

A

must be paid

not may be paid

86
Q

1.9 Glossary

Secular

Basic actuarial terminology

A

in relation to time measured by reference to the calender

example, the statement ‘Mortality can be expected to improve over an individual’s lifetime because of secular effects’, means that in the future people are likely to live longer than in previous generations, as over time, there are likely to be medical advances.

87
Q

1.9 Glossary

Duration

Basic actuarial terminology

A

in relation between two points in time

eg the time since you were born or since you took out your life insurance policy

88
Q

1.9 Glossary

Stochastic

Basic actuarial terminology

A

allowing for random variation over time

opposite of Deterministic

89
Q

1.9 Glossary

Deterministic

Basic actuarial terminology

A

not allowing for random variation over time

90
Q

1.9 Glossary

Per Annum

Basic actuarial terminology

A

per year

91
Q

1.9 Glossary

pa
pm
pcm
pq

Basic actuarial terminology

A

per annum
per month
per calcander year
per quarter

92
Q

1.9 Glossary

Pro Rata

Basic actuarial terminology

A

in proportion

93
Q

1.9 Glossary

Vice Versa

Basic actuarial terminology

A

the other way around

94
Q

1.9 Glossary

e.g.

Basic actuarial terminology

A

for example

95
Q

1.9 Glossary

i.e.

Basic actuarial terminology

A

that is

96
Q

1.9 Glossary

c.f.

Basic actuarial terminology

A

compare
eg. using the approximation, I got £73.98 (cf £74.02 when calculated accurately)

Actuarial Technician L4 (3 decks)

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