Stats

Question 1

what is a sample?

Answer 1

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

Question 2

what is the sampling frame?

Answer 2

to representation of the items availible to be sampled

Question 3

what is the sampling fraction?

Answer 3

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

Question 4

what is a census?

Answer 4

when the sampling fraction is 100%

Question 5

what does it mean to be random?

Answer 5

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

Question 6

what is a sampling error?

Answer 6

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

Question 7

describe simple random sampling

Answer 7

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

Question 8

describe stratified sampling

Answer 8

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

random,

Question 9

what is cluster sampling?

Answer 9

choosing from a limited number of clusters/ groups

Question 10

describe systematic sampling

Answer 10

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

Question 11

what is quota sampling?

Answer 11

• opportunity sampling within each group

Question 12

what is opportunity sampling?

Answer 12

first come, first served

Question 13

what is a variable?

Answer 13

something who’s value changes from one to another

Question 14

what notation is used for random variabes?

Answer 14

• capital letter (eg: X)
  *

Question 15

wht is distribution?

Answer 15

the pattern in which the variables occur

Question 16

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

Question 17

how would you identify an outlier

Answer 17

• if the item is more than 2 standard deviations from the mean
• the item is 1.5 times the IQR beyond the nearer quartile

Question 18

what is categorical/discrete data?

Answer 18

data which must be counted

eg: number of students

Question 19

what is continous data?

Answer 19

data which must be measured

Question 20

what is a discrete random variable?

Question 21

what do the lower case numbers represent?

Answer 21

particuar values that the random variables take.

Question 22

What is the sum of all probabilities?

Answer 22

Question 23

Answer 23

Question 24

What is a random variable ?

Answer 24

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

Question 25

Example of six sided fair die

Answer 25

Question 26

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

Answer 26

Discrete uniform distribution

Question 27

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

Answer 27

Question 28

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

Answer 28

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

Question 29

What is the expectation of a random variable?

Answer 29

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

Question 30

Finding the expected value

Answer 30

Question 31

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

Answer 31

Question 32

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Question 33

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Question 34

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Question 35

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Question 36

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Question 37

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

Answer 37

Question 38

What are the different forms of writing out the variance?

Answer 38

Question 39

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

Answer 39

Question 40

Answer 40

Question 41

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

Answer 41

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

Question 42

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

Answer 42

Question 43

Why are subscripts used with X?

Answer 43

Question 44

Why are subscripts used with X?

Answer 44

Question 45

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

Answer 45

Question 46

What is the difference between

Answer 46

Question 47

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Question 48

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Question 49

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Question 50

what is the poisson distribution?

Answer 50

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

Question 51

what is the probability function for poisson distribution?

Answer 51

Question 52

what is the shape of the poisson distribution?

Question 53

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

Answer 53

* **R**andom events * **I**ndependant 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 54

Question

Answer 54

Question 55

what are the properties of the poisson distribution?

Answer 55

* 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 56

Question 2

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Question 57

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Question 58

How do you add Poisson Variables?

Answer 58

Question 59

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Question 60

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

Answer 60

* Var(X)=λ * E(X)=λ a property of poisson distribution

Question 61

What is the representation/ deceleration of binomial distribution ?

Answer 61

X~B(n,p)

Question 62

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

Answer 62

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

Question 63

what are the conditions of binomial expansion?

Answer 63

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

Question 64

what is the formula for binomial distribution?

Answer 64

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