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maths > STATS AND MECHANICS > Flashcards

STATS AND MECHANICS Flashcards

1
Q

if y=a x^n , what is log y

A

log y= log a + n log x

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2
Q

if y= k b^x, what is log y

A

log y= log k + x log b

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3
Q

what does the product moment correlation coefficient describe

A

the linear correlation between 2 variables

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4
Q

values for PMCC

A

between -1 and 1

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5
Q

for a one tailed test of PMCC, what are the hypotheses

A

H0: ρ=0 H1: ρ<0
OR
H0: ρ=0 H1: ρ<0

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6
Q

for a two tailed test of PMCC, what are the hypotheses

A

H0: ρ=0
H1: ρ≠0

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7
Q

how can the event A and B be written

A

A∩B (intersection)

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8
Q

how can the event A or B be written

A

A∪B (union)

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9
Q

how can the event not A be written

A

A’ (complement of A)

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10
Q

how is the probability that B occurs given A occurs written

A

P(B|A)

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11
Q

for independent events what are P(A|B) and P(B|A)

A

P(A|B)= P(A|B’)=P(A)
P(B|A)=P(B|A’)=P(B)

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12
Q

equation for P(A∪B)

A

P(A∪B)=P(A)+P(B)-P(A∩B)

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13
Q

equation for P(B|A)

A

P(B∩A)/P(A)
so P(B∩A)= P(B|A) x P(A)

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14
Q

what is the area under a continuous probability distribution equal to

A

1

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15
Q

given the normal distribution is symmetrical, what is equal

A

the mean, median and mode

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16
Q

where are points of infection on normal distribution

A

μ+σ
μ-σ

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17
Q

standard normal distribution mean

A

0

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18
Q

standard normal distribution standard deviation

A

1

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19
Q

conditions required for binomial distribution to be approximated by the normal distribution

A

n is large (>50)
p is close to 0.5

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20
Q

equations to approximate the binomial distribution by the normal distribution

A

σ= sqrt (np(1-p))
μ= np

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21
Q

if you are using a normal approximation to a binomial distribution what do you need to apply when calculating probabilities

A

continuity correction

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22
Q

for a random sample size n taken from a random variable X-N(μ, σ^2), how is the sample mean distributed

A

X bar -N(μ,σ^2/n)

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23
Q

when using standard normal distribution, P(X<x)=p, what is equation with μ and σ

A

use P(X<x)=p and inverse normal using standard normal distribution to find A
x-Aσ=μ

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24
Q

equation for moment of F about P

A

|F| x perpendicular distance

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25
Q

what is the sum of moments acting on a body called

A

the resultant moment

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26
Q

when a rigid body is in equilibrium what is the resultant force and moment

A

resultant force in any direction in 0N
resultant moment in any direction is 0Nm

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27
Q

when a rigid body is on the point of tilting about a pivot, the reaction at any other support (or tension in any other wire or string) is what

A

0

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28
Q

where does mass act on a uniform rod

A

at midpoint

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29
Q

equation for maximum/limiting value of friction between 2 surfaces

A

Fmax=μR
μ= coefficient of friction
R= normal reaction between the 2 surfaces

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30
Q

what does the limiting value of friction depend on

A

the normal reaction R between the 2 surfaces in contact
the roughness of the 2 surfaces in contact

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31
Q

the rougher 2 surfaces in contact are, does μ become smaller or larger

A

larger

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32
Q

for smooth surfaces what is μ

A

no friction
μ=0

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33
Q

velocity of horizontal component of a projectile
therefore what equation can be made

A

constant velocity
a=0
s=vt

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34
Q

acceleration of vertical component of a projectile

A

constant acceleration due to gravoty
a=g

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35
Q

when a particle is projected with initial velocity U at an angle a above the horizontal, what are the components of the original velocity

A

horizontal component of initial velocity: U cosa
vertical component of initial velocity: U sina

36
Q

a particle reaches its point of greatest height when the vertical component of its velocity is what

A

0

37
Q

projectiles equation for time of flight
(initial velocity U, angle a above horizontal, projected from a point on a horizontal plane, moves freely under gravity)

A

(2U sin a) / g

38
Q

projectiles equation for time to reach greatest height
(initial velocity U, angle a above horizontal, projected from a point on a horizontal plane, moves freely under gravity)

A

(U sin a)/g

39
Q

projectiles equation for range on horizontal plane
(initial velocity U, angle a above horizontal, projected from a point on a horizontal plane, moves freely under gravity)

A

(U^2 sin 2a)/g

40
Q

when is a particle/rigid body in static equilibrium

A

it is at rest/stationary
resultant force acting on it in any direction is 0
resultant moment is 0

41
Q

which direction does friction act in

A

opposite to the direction in which the body would move if the frictional force were absent

42
Q

connected particles: what is the case if string is inextensible

A

acceleration of the particles is the same
tension in string is constant

43
Q

i and j are unit vectors due ____ and _____ (2D traditional)

A

east
north

44
Q

i and j are unit vectors acting ____ and _____ when using projectiles

A

horizontally
vertically

45
Q

if s= xi + yj, what is v
what is a

A

v= ds/dt= x’i +y’j
a= dv/dt= x’‘i +y’‘j

46
Q

what is a population

A

the whole set of items that are of interest

47
Q

what does a census do

A

observes or measures every member of a population

48
Q

what is a sample

A

a selection of observations taken from a subset of the population which is used to find out information about the population as a whole

49
Q

what are individual units of a population known as

A

sampling units

50
Q

what is a sampling frame

A

when sampling units of a population are individually names or numbered to form a list (sampling frame)

51
Q

what is a simple random sample

A

size n
one where every sample of size n has an equal chance of being selected

52
Q

what is systematic sampling

A

where the required elements are chosen at regular intervals to form an ordered list

53
Q

what is stratified sampling

A

the population is divided into mutually exclusive strata (e.g. males and females) and a random sample is taken from each

54
Q

what is quota sampling

A

an interviewer or researcher selects a sample that reflects the characteristics of the whole population

55
Q

what is opportunity sampling

A

consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for

56
Q

what is quantitative data

A

data associated with numerical observations

57
Q

what is qualitative data

A

data associated with non-numerical observations

58
Q

what is a continuous variable

A

a variable that can take any value in a given range

59
Q

what is a discrete variable

A

a variable that can take only specific values in a given range

60
Q

what are classes

A

when data is presented in a grouped frequency table, the specific data values are not shown
these groups are commonly known as classes

61
Q

variance equation

A

(Σ(x-x̄)^2)/n

or (Σx^2)/n - (Σx/n)^2

62
Q

standard deviation equation

A

square root of variance
sqrt (Σ(x-x̄)^2)/n

or sqrt (Σx^2)/n - (Σx/n)^2

63
Q

if data is coded using formula y= (x-a)/b, what is mean of coded data given by

A

ȳ= (x̄-a)/b

64
Q

if data is coded using formula y= (x-a)/b, what is standard deviation of coded data given by

A

σy= σx/b

65
Q

common definition of an outlier is any value that is:

A

> Q3+ k(Q3-Q1)
or
< Q1- k(Q3-Q1)

66
Q

what is cleaning the data

A

the process of removing anomalies

67
Q

how to calculate height of bar on a histogram (frequency density)

A

area of bar= k x frequency density

68
Q

what does joining the top of each bar in a histogram form

A

a frequency polygon

69
Q

what to comment on when comparing data sets

A

a measure of location
a measure of spread

70
Q

what is bivariate data

A

data which has pairs of values for 2 variables

71
Q

what does correlation describe

A

the nature of the linear relationship between 2 variables

72
Q

in what form is the regression Line of y on x written in

A

y= a + bx

73
Q

what is a Venn diagram used for

A

representing events graphically

74
Q

equation for mutually exclusive events

A

P (A or B)= P(A) + P(B)

75
Q

equation for independent events

A

P( A and B) = P(A) x P(B)

76
Q

what can a tree diagram be used to show

A

the outcomes of 2 or more events happening in succession

77
Q

what does a probability distribution describe

A

the probability of any outcome in the sample space

78
Q

conditions for modelling with binomial distribution

A

fixed number of trials, n
2 possible outcomes (success or failure)
fixed probability of success, p
trials are independent of each other

79
Q

what is the actual significance Level

A

the probability of incorrectly rejecting the null hypothesis

80
Q

what does the gradient represent on a displacement-time graph

A

the vleocity

81
Q

constant velocity on a displacement time graph?

A

straight line

82
Q

what does the gradient represent on a velocity-time graph

A

acceleration

83
Q

constant acceleration on a velocity time graph?

A

constant acceleration

84
Q

area between velocity time graph and horizontal axis represents what

A

distance travelled

85
Q

what does newtons first law state

A

an object at rest will stay at rest & an object moving with constant velocity will continue to move with constant velocity unless an unbalanced force acts on the object

86
Q

what does newtons second law state

A

the force needed to accelerate a particle is equal to the product of the mass of the particle and the acceleration produced:
F=ma

87
Q

how to solve problems involving connected particles

A

considering them separately OR
if they are moving in the same straight line consider them as a single particle

maths (4 decks)

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