Mathematical Models

Question 1

What is the role of statistical tests in mathematical modelling?

Answer 1

To assess how well a mathematical model matches a real world situation

Question 2

What are the 7 stages of mathematical modelling?

Answer 2

1. Real world problem observed
2. Mathematical model devised
3. Predictions made
4. Experimental data collected
5. Predictions compared to outcomes
6. Statistical test assesses success of model
7. Model is refined

Question 3

Advantages of mathematical models?

Answer 3

• Quick and easy to produce
• They can simplify a more complex situation
• They enable predictions to be made about the future

Question 4

Disadvantages of mathematic models?

Answer 4

• They only give a partial description of the real situation

* They only work for a restricted range of values

Question 5

Continuous variable

Answer 5

A variable which can take any value in a given range

Question 6

Discrete variable

Answer 6

A variable that can only take values within a given range

Question 7

How to find median in discrete data?

Answer 7

Divide n by 2

Question 8

How to find the median in continuous data?

Answer 8

Divide n by 2, and then use interpolation to find the exact term

Question 9

What is the height of a histogram bar?

Answer 9

Frequency density

Question 10

What is frequency density?

Answer 10

Frequency ÷ class width

Question 11

Which data are histograms used to display?

Answer 11

Continuous

Question 12

Ways to describe skew of data?

Answer 12

•Shape from box plots

• 3(mean-median)
————————
Standard deviation

Question 13

P(A’)=…

Answer 13

= 1- P(A)

Question 14

P (A U B) =…

Answer 14

= P(A) + P(B) - P(A ∩ B)

and vice versa

Question 15

P(A|B) =…

Answer 15

= P(A∩B)
————
P(B)

Question 16

P(A∩B)=…

Answer 16

P(A|B) x P(B) or P(B|A) x P(A)

Question 17

When are A and B independent?

Answer 17

P(A|B) = P(A)

or

P(A∩B) = P(A) x P(B)

Question 18

When are A and B mutually exclusive?

Answer 18

P(A∩B) = 0

Question 19

What does a represent in a regression line?

Answer 19

The point at which y touches the x axis

Question 20

What does b represent on in a regression line?

Answer 20

The amount by which y increase for an increase of 1 in x (gradient)

Question 21

What is an independent/explanatory variable?

Answer 21

One which is set independently of the other variable

Question 22

What is a dependent/response variable?

Answer 22

One whose value are determined by the values of the independent variable

Question 23

How to calculate b in the regression line?

Answer 23

Sxy
———
Sxx

Question 24

P(A’)=…

Answer 24

= 1- P(A)

Question 25

P (A U B) =…

Answer 25

= P(A) + P(B) - P(A ∩ B)

and vice versa

Question 26

P(A|B) =…

Answer 26

= P(A∩B)
————
P(B)

Question 27

P(A∩B)=…

Answer 27

P(A|B) x P(B) or P(B|A) x P(A)

Question 28

When are A and B independent?

Answer 28

P(A|B) = P(A)

or

P(A∩B) = P(A) x P(B)

Question 29

When are A and B mutually exclusive?

Answer 29

P(A∩B) = 0

Question 30

What does a represent in a regression line?

Answer 30

The point at which y touches the x axis

Question 31

What does b represent on in a regression line?

Answer 31

The amount by which y increase for an increase of 1 in x (gradient)

Question 32

What is an independent/explanatory variable?

Answer 32

One which is set independently of the other variable

Question 33

What is a dependent/response variable?

Answer 33

One whose value are determined by the values of the independent variable

Question 34

How to calculate b in the regression line?

Answer 34

Sxy
———
Sxx

Question 35

How to calculate a in the regression line?

Answer 35

a= (mean of y) - b( mean of x)

Question 36

Interpolation

Answer 36

Estimate of the value of the dependent variable within the range of the data

Question 37

Extrapolation

Answer 37

When you estimate a value outside the range of data

Question 38

What is an important property of discrete random variables?

Answer 38

Sum of them =1

Question 39

How to find F(x)?

Answer 39

Add together all the for all those outcomes which are less than or equal to x

Question 40

What is E(X)?

Answer 40

ΣxP(X=x) or mean

Question 41

What is Var(X)?

Answer 41

Var(X) = E(X^2) - E(X)^2

Question 42

What are the conditions for a discrete uniform distribution?

Answer 42

• Each value is equally likely

* A dislike random variable X is defined over a set of n values

Question 43

What is the E(X) for a discrete uniform distribution?

Answer 43

E(X) = n+1
——
2

where n is the final value of x

Question 44

How to calculate Var(X) for a discrete uniform distribution?

Answer 44

(n+1)(n-1)
Var(X) = —————
12

where n is the final value of x