Brainscape's Knowledge GenomeTM

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


See full index

Maths - S2 > Definitions > Flashcards

Definitions Flashcards

1
Q 
CRV E(X)=
Var(X)=
A

0.5(b+a) or integrate between boundaries and * x

1/12(b-a)^2 or integrate and *x^2 - mean^2

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

Conditions of binomial

A

fixed number of trials

constant probability, independent trial, two outcomes

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

Conditions of poisson

A

singly, constant rate, independantly

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

Census =

A

investigation of every member or population

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

Sampling unit =

A

individual member/element of population

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

Sampling frame =

A

list of all the populations/sakmpling units e.g. name or unique ID

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

Sampling distribution =

A

set of all possible values of the statistic together with their individual probabilities

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

Why are samples better than a census

A

quicker and a census would use up all elements of sample

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

mode =

A

value of x at which maximum occurs, dy/dx = 0

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

Median =

A

F(median) =0.25

integrate pdf

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

-ve skew means

A

mean less than median less than mode
Q3-Q2 less than Q2-Q1
quadratic up straight line down

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

When doing a pdf

A

draw points when y=0

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

Population =

A

collection of all items

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

Sample =

A

subset of population intended to represent the population

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

B —> Po

A

n large > 50 p small <0.2

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

B—-> N

A

Continuity correction (as discrete to continuous)
n large (n>50)
p close to 0.5
(np>5, nq>5)

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

Po—-N

A

lambda large (>20)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Po—-B

A

if only 3ish marks

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

X-Po(3)
P(X=2) = 0.5
X-Po(6)
P(X=2) =

A

0.5^2 = 0.25

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

Poisson P(1<=X<=4) =

A

P(X<=4) - P(X<1)

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

Statisitic =

A

a r.v. which is some function of a sample and not dependant on any parameters e.g. not mu or sigma but x bar is fine

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

Sampling distribution =

A

Probability distribution of all values

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

Hypothesis test =

A

mathematical procedure to examine a value of a population parameter proposed by the null hypothesis compared with an alternative hypothesis

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

Critical region =

A

range of values of a test statistic which would provide enough evidence to reject the null hypothesis

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

If for top tail P(X<=9) > 0.95 then

A

X>=10

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

Actual significance level means

A

add values up and should be nearish original significance level

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

When drawing a ‘suitable pdf’

A

think about skewness and logic not always exact normal distribution bell curve for example

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

In hypothesis testing can be more than or less than significance level but should be

A

as close as possible to it

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Why do a CCC

A

Due to going from discrete to continuous so making up for gaps

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

P(|X|<1.5) =

A

P(-1.5 less than x less than 1.5)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

2 tail bottom or top

A

Np < value top

Np > value bottom

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

Significance level in two tail is

A

Half of original

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

+skew means

A

mean>median>mode
Q3-Q2>Q2-Q1
Majority of data on left
Right tail longer

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

Finite population

A

A population is one in which each individual member can be given a number
(a population might be so large that it is difficult or impossible to give each member a number –
e.g. grains of sand on the beach).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

Infinite population

A

A population is one in which each individual member cannot be given a number.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

Simple random sample

A

A simple random sample of size n, is one taken so that every possible sample of size n has an
equal chance of being selected.
The members of the sample are independent random variables, X1, X2, … , Xn , and each Xi has
the same distribution as the population

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

Sample

A

A selection of sampling units from the sampling frame

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

Sample survey

A

An investigation using a sample

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

Advantages of a census

A

Every member of the population is used.
It is unbiased.
It gives an accurate answer.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

Disadvantages of a census

A

It takes a long time.
It is costly.
It is often difficult to ensure that the whole population is surveyed.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

Advantages of sampling

A

Sample will be representative if population large and well mixed.
Usually cheaper.
Essential if testing involves destruction (life of a light bulb, etc.).
Data usually more easily available

42
Q

Disadvantages of sampling

A

Uncertainty, due to the natural variation – two samples are unlikely to give the same result.
Uncertainty due to bias prevents the sample from giving a representative picture of the population

43
Q

Bias comes from

A

subjective choice
incomplete sampling frame

*bias cannot be removed by increasing the size of the sample

44
Q

Always remember

A

Define random variable
Give in context
+C
Continuity correction as discrete to continuous
Square root variance in normal distribution

45
Q

Conditions of normal

A 
Median = mean = mode
Area under curve = 1
Bell shaped
Symmetrical 
Mean and standard deviation parameters
46
Q

mean =

variance =

A

x * P(X=x) or n*p

x^2 * P(X=x) - mean^2 or n^2p - (np)^2

47
Q

P(5<=X<7)

A

P(X<=6) - P(X<=4)

48
Q

Var(X+Y)

E(X+Y)

A

Var(X) + Var(Y)

E(X) + E(Y)

49
Q

conditions for Binomial to Normal

A

n large p close to 0.5
np > 5
n(1-p) = npq > 5

50
Q

Critical regions and Critical values are

A

Critical values are two specific values while the region is everything inside as well

51
Q

Countably infinite population =

A

infinite size but each member can be given an individual member

52
Q

Sample mean is…. the population mean

Sample variance is… the population variance

A

equal to

less than

53
Q

Random sample =

A

every possibility has equal chance

Randint#(1,50)

54
Q

Coin = Binomial =

A

(n, 0.5)

55
Q

What is the most accurate p for B–>N

A

0,,5 so the binomial distribution is reasonably symmetrical

56
Q

Y = Xbar =

A

sumx/n = statistic (X bar is allowed but mu is not)

57
Q

Population does not always equal the sampling frame because

A

it is not always possible to keep this list up to date

58
Q

Most accurate approximation is one which

A

most closely meets the requirements of approximation e.g. how close p is to 0.5

59
Q

CRV P(X=a) =

A

0 as not a probability density function

60
Q

Poisson events are independent so will occur again at the same rate in the same time

A

So just square the value or cube etc…

61
Q

n! =

A

number of ways of ordering a collection of n objects

62
Q

nCr =

A

n!/(n-r)!r! = number of ways selecting r objects from n

63
Q

Why is Poisson to normal when lambda is large

A

because distribution would be fairly symmetrical

64
Q 
CRV = pdf = 
DRV = pd =
A

probability density function

probability distribution

65
Q

Always show that x = 0 on a

A

pdf

66
Q

Var(X) =

A

E(X^2) - E(X)^2

67
Q

E(X^2) =

A

Var(X) + E(X)^2

68
Q

P(X=4)

A

P(X<=4) - P(X<=3) = F(4) - F(3)

69
Q

P(X>E(X)) > 0.5 therefore

A

mean less than median therefore negative skew

70
Q

For two tailed test when not finding critical region make an educated guess on whether > than or < than or just do critical region for both sides

A

does not equal

half if doing both sides but if just one side then dont

71
Q

E(X) =

A 
integrate f(x)*x NOT integrate F(X)
must be f(x) so differentiate if need be
72
Q

E(X^2) =

A 
integrate f(x)*x^2 
NOT F(x)
73
Q

E(-X^2 + 9X) =

A

E(-X^2) + E(9X) = 9E(X) - E(X^2)

74
Q

P(X>k) = P(Y

A

P(Y>n-k)

75
Q

P(X>k) =

A

P(Y>n-k)

76
Q

P(4<=X<=8) =

A

P(X<=8) - P(X<=3) draw number line with squares at midpoints of numbers rather than lines

77
Q

J-U[a, b]

A

Uniform

78
Q

Discrete to continuous P(X=5) =

A

P(4.5<=X<=5.5)

79
Q

X-B(100,0.975) approximation

A

Poisson

80
Q

Significance level =

A

probability of incorrectly rejecting H0

81
Q

Read question if as close as possible to

A

significance level

82
Q

Sampling frame =

A

identifier

83
Q

Statistic does not equal

A

mu or sigma

84
Q

P(mu - ksigma less than X less than mu + ksigma) = 0.5

A 
P(Q1 < X < Q3) = 0.5
therefore mu+ ksigma = Q3 etc
or P(X = k) = 0.75
85
Q

key words for poisson

A

rate and randomly scattered

86
Q

CRV:
P(X=5)=
P(X>=10) =

A

0

1-P(X<=10)

87
Q

DRV P(x>=10) =

A

1-P(X<=9)

88
Q

P(X…) is very low then

A

unlikely that parameter probability (p) is correct

89
Q

P(X’)^2 =

A

1 - P(X)^2

NOT (1-P(X))^2

90
Q

Always check F(X) =

A

0, 1, previous

and remember +C

91
Q

F(x) put (0,1) at

A

maximum of sketch

92
Q

2 minutes added to all values find new median and variance

A 
E(X+2) = E(X) + 2 
Var(X+2) = Var(X)
93
Q

F(min x value) =

A

0

94
Q

Mode =

A

minimum x value

95
Q

Justify mode is maximum via

A

second derivative

96
Q

E(5x^2) =

A

5E(X^2)

97
Q

Given that X=4 over 2 days

Find X=1 on day 1 and X=3 on day 2

A

X-Po(1 per day)
P(X=1) * P(X=4) when X-Po(1)
divided by P(X=4) when X-Po(2)

98
Q

Find the probability that 1 car after another car in less than 2 days

A

X-Po(2 days)

P(more than 1 cars) = P(X>=1)

99
Q

Try not to have an unrounded value when going from discrete to normal distribution for continuity correction

A

Round to 0 decimal places

100
Q

Diagram for binomial or Poisson is

A

Prob y axis
number of events x axis
vertical lines with spaces

Maths - S2 (1 decks)

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