S2

Question 0

Binomial Distribution

Conditions

Answer 0

Fixed number of trials
Independent trials
Constant probability of success
Two possible outcomes

Question 1

Binomial Distribution

Notation

Answer 1

X~B (n,p)

n = number of trials 
p = probability of success

Question 2

Binomial Distribution

Formula

Answer 2

P(X = r) = nCr x p^r x q^n-R

Question 3

Binomial Distribution

Expectation

Answer 3

E(X) = np

Question 4

Binomial Distribution

Variance

Answer 4

Var(X) = npq

Question 5

Binomial Distribution

Poisson Approximation

Answer 5

If n is large and p is small
Then
X~B (n,p) ≈ Y~Po(np)

Question 6

Binomial Distribution

Normal Approximation

Answer 6

If n is large, np>5 and nq>5
Then
X~B (n,p) ≈ Y~N (np,npq)

Using a half continuity correction

Question 7

Poisson Distribution

Notation

Answer 7

X~Po (λ)

Question 8

Poisson Distribution

Conditions

Answer 8

Events occur independently, singly and at a constant rate

Question 9

Poisson Distribution

Formula

Answer 9

P(X =r) = (e^-λ x λ^r) / r!

Question 10

Poisson Distribution

Expectation

Answer 10

E(X) = λ

Question 11

Poisson Distribution

Variance

Answer 11

Var(X) = λ

Question 12

Poisson Distribution

Normal Approximation

Answer 12

If λ>10
Then
X~Po (λ) ≈ Y~N (λ,λ)

Question 13

Probability Density Function

Properties

Answer 13

f(x) ≥ 1 for all values of x

The area under the line = 1

Question 14

PDF

Notation

Answer 14

f(x) =
function of x, a≤x≤b
0, otherwise

Question 15

Cumulative Distribution Function

Properties

Answer 15

0 ≤ F(x) ≤ 1
Area at start = 0
Area at end = 0

Question 16

CDF

Notation

Answer 16

F(x) =

0, a<b

Question 17

CDF to PDF

Answer 17

Differentiate

Question 18

PDF to CDF

Answer 18

Integrate

Remember c

Question 19

Continuous Random Variable

Mode

Answer 19

Maximum value of f(x)

Question 20

Continuous Random Variable

Median

Answer 20

F(m) = 0.5

Question 21

Continuous Random Variable

Mean

Answer 21

Multiply PDF by x then integrate between the bonds

Question 22

Continuous Random Variable

Variance

Answer 22

(Multiply PDF by x² then integrate between the bounds) - mean²

Question 23

Continuous Uniform Distribution

PDF

Answer 23

1 / b-a

Question 25

Continuous Uniform Distribution

PDF shape

Answer 25

Straight horizontal line

Question 26

Continuous Uniform Distribution

Median

Answer 26

(a+b) / 2

Question 27

Continuous Uniform Distribution

Mean

Answer 27

(a+b) / 2

Question 28

Continuous Uniform Distribution

Variance

Answer 28

(b - a)² / 12

Question 29

Sampling

Benefits

Answer 29

Representative
Useful when the test would harm or damage the item
Cheap
Quick

Question 30

Sampling

Restrictions

Answer 30

Natural variation

Bias

Question 30

Population

Definition

Answer 30

Collection of individuals or items

Question 31

Finite Population

Definition

Answer 31

A population for which the number of members can be known

Question 32

Infinite Population

Definition

Answer 32

A population for which the number of members cannot be known

Question 33

Census

Definition

Answer 33

Taking information from every member of the population

Question 34

Sample

Definition

Answer 34

A selection of members form the population

Can be any size

Question 35

Sampling Unit

Definition

Answer 35

A member of the sample

Question 36

Sample Frame

Definition

Answer 36

List of all the possible sampling units in the population

Question 37

Statistic

Definition

Answer 37

A function of the observations and no other values

Question 38

Critical Region

Definition

Answer 38

The range of values for which the null hypothesis is rejected

Question 39

Significance Level

Definition

Answer 39

The probability used for very unlikely