Stats Flashcards
what is a sample?
something that provides a set of data values of a random variable, drawn from all possible values (population)
what is the sampling frame?
to representation of the items availible to be sampled
what is the sampling fraction?
the proprtion of availiable items that are actually sampled.
* sample size/ population size
what is a census?
when the sampling fraction is 100%
what does it mean to be random?
each item in the population has an equal probability of being included in the sample
what is a sampling error?
the difference between the true value and the value derived from sample data
describe simple random sampling
- population numbered from 1-n
- random numbers are generated from 1-n
- corresponding members of the population are selected
(discard repeats)
random, sampling frame required
describe stratified sampling
- from each group in population
- SRS conducted within each group
random,
what is cluster sampling?
choosing from a limited number of clusters/ groups
describe systematic sampling
- items numbered from 1-n
- choose a random starting point
- every kth value forms the corresponding sample
random, sampling frame required, list should not be ordered with bias
what is quota sampling?
- opportunity sampling within each group
what is opportunity sampling?
first come, first served
what is a variable?
something who’s value changes from one to another
what notation is used for random variabes?
- capital letter (eg: X)
*
wht is distribution?
the pattern in which the variables occur
draw graphs for the terms:
* unimodal
* positive skew
* negative skew
* bimodal
how would you identify an outlier
- if the item is more than 2 standard deviations from the mean
- the item is 1.5 times the IQR beyond the nearer quartile
what is categorical/discrete data?
data which must be counted
eg: number of students
what is continous data?
data which must be measured
what is a discrete random variable?
what do the lower case numbers represent?
particuar values that the random variables take.
What is the sum of all probabilities?
What is a random variable ?
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
Example of six sided fair die
Draw the probability distribution of X- for a fair six sided die
Discrete uniform distribution
What is the function form of the probability of X (fair 6 sided die)?
What are the properties for a probability distribution to be valid?
All probabilities must be greater than or equal to zero. The sum of all probabilities must be equal to 1.
What is the expectation of a random variable?
The expected value of a random variable, which is the mean if a frequency distribution and will be referred to as the mean
Finding the expected value
What is the formula of variance for a discrete random variable?
What are the differences forms of writing out the mean (expected value )?
What are the different forms of writing out the variance?
What is the expectation of aX + b? (Proof Version)
What is the variance of aX+b ? (In proof form)
No b as this should not impact spread.
a is squared a standard deviation is a squared Measure
How is the sum of two random variables (not constants) treated in expected value ?
Why are subscripts used with X?
Why are subscripts used with X?
What are the rules for variance with more than 1 random variable ?
What is the difference between
what is the poisson distribution?
used for counting the events that occur randomly in a given interval of time
what is the probability function for poisson distribution?
what is the shape of the poisson distribution?
let X represent the number of occurences per interval of time or space.
what following conditions must be fufilled to model a poisson distribution?
- 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
Question
what are the properties of the poisson distribution?
- 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
Question 2
How do you add Poisson Variables?
what is the variance and mean of the X~Po(λ)?
- Var(X)=λ
- E(X)=λ
a property of poisson distribution
What is the representation/ deceleration of binomial distribution ?
X~B(n,p)
What does
X~B(n,p) mean?
let randon variable X be distributed binomially with n trials, each with a probability of P success
what are the conditions of binomial expansion?
- F ixed number of trials (n)
- I ndependant trials
- C onstant probability of success
- T wo possible outcomes only- sucess or fail
what is the formula for binomial distribution?
N choose r, p to the power of r, one minus p to the power of n minus r
