Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

A Level Further maths > Stats > Flashcards

Stats Flashcards

1
Q

what is a sample?

A

something that provides a set of data values of a random variable, drawn from all possible values (population)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

what is the sampling frame?

A

to representation of the items availible to be sampled

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

what is the sampling fraction?

A

the proprtion of availiable items that are actually sampled.
* sample size/ population size

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

what is a census?

A

when the sampling fraction is 100%

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

what does it mean to be random?

A

each item in the population has an equal probability of being included in the sample

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

what is a sampling error?

A

the difference between the true value and the value derived from sample data

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

describe simple random sampling

A
  1. population numbered from 1-n
  2. random numbers are generated from 1-n
  3. corresponding members of the population are selected
    (discard repeats)

random, sampling frame required

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

describe stratified sampling

A
  1. from each group in population
  2. SRS conducted within each group

random,

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

what is cluster sampling?

A

choosing from a limited number of clusters/ groups

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

describe systematic sampling

A
  1. items numbered from 1-n
  2. choose a random starting point
  3. every kth value forms the corresponding sample

random, sampling frame required, list should not be ordered with bias

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

what is quota sampling?

A
  • opportunity sampling within each group
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

what is opportunity sampling?

A

first come, first served

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

what is a variable?

A

something who’s value changes from one to another

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what notation is used for random variabes?

A
  • capital letter (eg: X)
    *
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

wht is distribution?

A

the pattern in which the variables occur

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

draw graphs for the terms:
* unimodal
* positive skew
* negative skew
* bimodal

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

how would you identify an outlier

A
  • if the item is more than 2 standard deviations from the mean
  • the item is 1.5 times the IQR beyond the nearer quartile
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

what is categorical/discrete data?

A

data which must be counted

eg: number of students

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

what is continous data?

A

data which must be measured

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

what is a discrete random variable?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

what do the lower case numbers represent?

A

particuar values that the random variables take.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is the sum of all probabilities?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q
A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

What is a random variable ?

A

A variables whose value is subject to variations due to chance. It can take a set of possible different values each with an associated probability

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Example of six sided fair die

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Draw the probability distribution of X- for a fair six sided die

A

Discrete uniform distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

What is the function form of the probability of X (fair 6 sided die)?

A
28
Q

What are the properties for a probability distribution to be valid?

A

All probabilities must be greater than or equal to zero. The sum of all probabilities must be equal to 1.

29
Q

What is the expectation of a random variable?

A

The expected value of a random variable, which is the mean if a frequency distribution and will be referred to as the mean

30
Q

Finding the expected value

A
31
Q

What is the formula of variance for a discrete random variable?

A
32
Q
A
33
Q
A
34
Q
A
35
Q
A
36
Q
A
37
Q

What are the differences forms of writing out the mean (expected value )?

A
38
Q

What are the different forms of writing out the variance?

A
39
Q

What is the expectation of aX + b? (Proof Version)

A
40
Q
A
41
Q

What is the variance of aX+b ? (In proof form)

A

No b as this should not impact spread.
a is squared a standard deviation is a squared Measure

42
Q

How is the sum of two random variables (not constants) treated in expected value ?

A
43
Q

Why are subscripts used with X?

A
44
Q

Why are subscripts used with X?

A
45
Q

What are the rules for variance with more than 1 random variable ?

A
46
Q

What is the difference between

A
47
Q
A
48
Q
A
49
Q
A
50
Q

what is the poisson distribution?

A

used for counting the events that occur randomly in a given interval of time

51
Q

what is the probability function for poisson distribution?

A
52
Q

what is the shape of the poisson distribution?

A
53
Q

let X represent the number of occurences per interval of time or space.
what following conditions must be fufilled to model a poisson distribution?

A
  • Random events
  • Independant events
  • ** A** verage number of events(λ) given is fixed and finite,
  • eg: number of phone calls on a random chosen day
  • eg: number of accidents in a factory per month
54
Q

Question

A
55
Q

what are the properties of the poisson distribution?

A
  • The average number of events in the given interval (λ) is fixed and finite.
  • if interval in time/space is scaled up or down, the average rate (λ) is correspondingly scaled
56
Q

Question 2

A
57
Q
A
58
Q

How do you add Poisson Variables?

A
59
Q
A
60
Q

what is the variance and mean of the X~Po(λ)?

A
  • Var(X)=λ
  • E(X)=λ
    a property of poisson distribution
61
Q

What is the representation/ deceleration of binomial distribution ?

A

X~B(n,p)

62
Q

What does
X~B(n,p) mean?

A

let randon variable X be distributed binomially with n trials, each with a probability of P success

63
Q

what are the conditions of binomial expansion?

A
  • F ixed number of trials (n)
  • I ndependant trials
  • C onstant probability of success
  • T wo possible outcomes only- sucess or fail
64
Q

what is the formula for binomial distribution?

A

N choose r, p to the power of r, one minus p to the power of n minus r

65
Q
A

A Level Further maths (10 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions