Statistics
Chapter 5 – pairs of variables
Two variables are most often called; X and Y. to be able to do this, there are some things that have to
be distinguished
1) Both variables are quantitative
2) Both variables are qualitative
3) One is quantitative and the other is qualitative
Studying the dependence of the data of one variable (eg; Y), on the data of the other variable -> you
need to ask yourself whether, how & to what extent the data of Y depends on the data of X
Chapter 6 – definitions of probability
For probabilities to exist, chance & uncertainty are necessary
Random experiment = an experimentation r an uncontrollable phenomenon for which more than
one outcome is possible. The result of a random experiment is not known with certainty in advance -
> because it is partially determined by chance
The possible reults of a random experiment are called the (possible) outcomes, the set of all
the possible outcomes is the sample space (Ω)
Sample space is also called omega Ω
Example 1 of a random experiment is to throw a die. The results that you can get are; 1,2,3,4,5,6 –
this is written down in the sample space as ; Ω = {1,2,3,4,5,6}
- The brackets note that a set is involved
- The outcomes from 1-6 are the elements of the set
- Chance determines which of the 6 outcomes will occur
Example 2; flipping a coin. You have 2 possible outcomes; head (H) and tail (T). chance determines
which one will occur
Population size is denoted in statistics as N
Subsets are part of the sample space, so for instance when throwing a die. If you need a 5 or 6 to win
the game, you would want to throw one of these sides of the die. This specific interest in the subset
of the entire sample space is named an event.
A certain event, so a subset of Ω can occur if the actual outcome of the experiment belongs
to that event.
Events with exactly 1 outcome are called single events
Events with more than 1 outcome are called multiple events
Note that Ω in itself, is also an event, this event will always occur since the actual outcome of
the experiment will always fall within the sample space Ω
An empty event Ø = is a subset that does not contain any outcomes. This is a subset of sample space
Ω, is a matter logic – to be able to be a subset of Ω, all elements have to be an outcome in Ω. But
since the fact that the empty event Ø has no elements, this is automatically also the case for the
subset Ø
Chapter 5 – pairs of variables
Two variables are most often called; X and Y. to be able to do this, there are some things that have to
be distinguished
1) Both variables are quantitative
2) Both variables are qualitative
3) One is quantitative and the other is qualitative
Studying the dependence of the data of one variable (eg; Y), on the data of the other variable -> you
need to ask yourself whether, how & to what extent the data of Y depends on the data of X
Chapter 6 – definitions of probability
For probabilities to exist, chance & uncertainty are necessary
Random experiment = an experimentation r an uncontrollable phenomenon for which more than
one outcome is possible. The result of a random experiment is not known with certainty in advance -
> because it is partially determined by chance
The possible reults of a random experiment are called the (possible) outcomes, the set of all
the possible outcomes is the sample space (Ω)
Sample space is also called omega Ω
Example 1 of a random experiment is to throw a die. The results that you can get are; 1,2,3,4,5,6 –
this is written down in the sample space as ; Ω = {1,2,3,4,5,6}
- The brackets note that a set is involved
- The outcomes from 1-6 are the elements of the set
- Chance determines which of the 6 outcomes will occur
Example 2; flipping a coin. You have 2 possible outcomes; head (H) and tail (T). chance determines
which one will occur
Population size is denoted in statistics as N
Subsets are part of the sample space, so for instance when throwing a die. If you need a 5 or 6 to win
the game, you would want to throw one of these sides of the die. This specific interest in the subset
of the entire sample space is named an event.
A certain event, so a subset of Ω can occur if the actual outcome of the experiment belongs
to that event.
Events with exactly 1 outcome are called single events
Events with more than 1 outcome are called multiple events
Note that Ω in itself, is also an event, this event will always occur since the actual outcome of
the experiment will always fall within the sample space Ω
An empty event Ø = is a subset that does not contain any outcomes. This is a subset of sample space
Ω, is a matter logic – to be able to be a subset of Ω, all elements have to be an outcome in Ω. But
since the fact that the empty event Ø has no elements, this is automatically also the case for the
subset Ø
