STATS AND MECHANICS Flashcards
if y=a x^n , what is log y
log y= log a + n log x
if y= k b^x, what is log y
log y= log k + x log b
what does the product moment correlation coefficient describe
the linear correlation between 2 variables
values for PMCC
between -1 and 1
for a one tailed test of PMCC, what are the hypotheses
H0: ρ=0 H1: ρ<0
OR
H0: ρ=0 H1: ρ<0
for a two tailed test of PMCC, what are the hypotheses
H0: ρ=0
H1: ρ≠0
how can the event A and B be written
A∩B (intersection)
how can the event A or B be written
A∪B (union)
how can the event not A be written
A’ (complement of A)
how is the probability that B occurs given A occurs written
P(B|A)
for independent events what are P(A|B) and P(B|A)
P(A|B)= P(A|B’)=P(A)
P(B|A)=P(B|A’)=P(B)
equation for P(A∪B)
P(A∪B)=P(A)+P(B)-P(A∩B)
equation for P(B|A)
P(B∩A)/P(A)
so P(B∩A)= P(B|A) x P(A)
what is the area under a continuous probability distribution equal to
1
given the normal distribution is symmetrical, what is equal
the mean, median and mode
where are points of infection on normal distribution
μ+σ
μ-σ
standard normal distribution mean
0
standard normal distribution standard deviation
1
conditions required for binomial distribution to be approximated by the normal distribution
n is large (>50)
p is close to 0.5
equations to approximate the binomial distribution by the normal distribution
σ= sqrt (np(1-p))
μ= np
if you are using a normal approximation to a binomial distribution what do you need to apply when calculating probabilities
continuity correction
for a random sample size n taken from a random variable X-N(μ, σ^2), how is the sample mean distributed
X bar -N(μ,σ^2/n)
when using standard normal distribution, P(X<x)=p, what is equation with μ and σ
use P(X<x)=p and inverse normal using standard normal distribution to find A
x-Aσ=μ
equation for moment of F about P
|F| x perpendicular distance
what is the sum of moments acting on a body called
the resultant moment
when a rigid body is in equilibrium what is the resultant force and moment
resultant force in any direction in 0N
resultant moment in any direction is 0Nm
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
0
where does mass act on a uniform rod
at midpoint
equation for maximum/limiting value of friction between 2 surfaces
Fmax=μR
μ= coefficient of friction
R= normal reaction between the 2 surfaces
what does the limiting value of friction depend on
the normal reaction R between the 2 surfaces in contact
the roughness of the 2 surfaces in contact
the rougher 2 surfaces in contact are, does μ become smaller or larger
larger
for smooth surfaces what is μ
no friction
μ=0
velocity of horizontal component of a projectile
therefore what equation can be made
constant velocity
a=0
s=vt
acceleration of vertical component of a projectile
constant acceleration due to gravoty
a=g
when a particle is projected with initial velocity U at an angle a above the horizontal, what are the components of the original velocity
horizontal component of initial velocity: U cosa
vertical component of initial velocity: U sina
a particle reaches its point of greatest height when the vertical component of its velocity is what
0
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)
(2U sin a) / g
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)
(U sin a)/g
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)
(U^2 sin 2a)/g
when is a particle/rigid body in static equilibrium
it is at rest/stationary
resultant force acting on it in any direction is 0
resultant moment is 0
which direction does friction act in
opposite to the direction in which the body would move if the frictional force were absent
connected particles: what is the case if string is inextensible
acceleration of the particles is the same
tension in string is constant
i and j are unit vectors due ____ and _____ (2D traditional)
east
north
i and j are unit vectors acting ____ and _____ when using projectiles
horizontally
vertically
if s= xi + yj, what is v
what is a
v= ds/dt= x’i +y’j
a= dv/dt= x’‘i +y’‘j
what is a population
the whole set of items that are of interest
what does a census do
observes or measures every member of a population
what is a sample
a selection of observations taken from a subset of the population which is used to find out information about the population as a whole
what are individual units of a population known as
sampling units
what is a sampling frame
when sampling units of a population are individually names or numbered to form a list (sampling frame)
what is a simple random sample
size n
one where every sample of size n has an equal chance of being selected
what is systematic sampling
where the required elements are chosen at regular intervals to form an ordered list
what is stratified sampling
the population is divided into mutually exclusive strata (e.g. males and females) and a random sample is taken from each
what is quota sampling
an interviewer or researcher selects a sample that reflects the characteristics of the whole population
what is opportunity sampling
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
what is quantitative data
data associated with numerical observations
what is qualitative data
data associated with non-numerical observations
what is a continuous variable
a variable that can take any value in a given range
what is a discrete variable
a variable that can take only specific values in a given range
what are classes
when data is presented in a grouped frequency table, the specific data values are not shown
these groups are commonly known as classes
variance equation
(Σ(x-x̄)^2)/n
or (Σx^2)/n - (Σx/n)^2
standard deviation equation
square root of variance
sqrt (Σ(x-x̄)^2)/n
or sqrt (Σx^2)/n - (Σx/n)^2
if data is coded using formula y= (x-a)/b, what is mean of coded data given by
ȳ= (x̄-a)/b
if data is coded using formula y= (x-a)/b, what is standard deviation of coded data given by
σy= σx/b
common definition of an outlier is any value that is:
> Q3+ k(Q3-Q1)
or
< Q1- k(Q3-Q1)
what is cleaning the data
the process of removing anomalies
how to calculate height of bar on a histogram (frequency density)
area of bar= k x frequency density
what does joining the top of each bar in a histogram form
a frequency polygon
what to comment on when comparing data sets
a measure of location
a measure of spread
what is bivariate data
data which has pairs of values for 2 variables
what does correlation describe
the nature of the linear relationship between 2 variables
in what form is the regression Line of y on x written in
y= a + bx
what is a Venn diagram used for
representing events graphically
equation for mutually exclusive events
P (A or B)= P(A) + P(B)
equation for independent events
P( A and B) = P(A) x P(B)
what can a tree diagram be used to show
the outcomes of 2 or more events happening in succession
what does a probability distribution describe
the probability of any outcome in the sample space
conditions for modelling with binomial distribution
fixed number of trials, n
2 possible outcomes (success or failure)
fixed probability of success, p
trials are independent of each other
what is the actual significance Level
the probability of incorrectly rejecting the null hypothesis
what does the gradient represent on a displacement-time graph
the vleocity
constant velocity on a displacement time graph?
straight line
what does the gradient represent on a velocity-time graph
acceleration
constant acceleration on a velocity time graph?
constant acceleration
area between velocity time graph and horizontal axis represents what
distance travelled
what does newtons first law state
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
what does newtons second law state
the force needed to accelerate a particle is equal to the product of the mass of the particle and the acceleration produced:
F=ma
how to solve problems involving connected particles
considering them separately OR
if they are moving in the same straight line consider them as a single particle
