1.3 Definition of Probability
In the statistical investigation, we observe the part of the population and then estimate the parameter for the population.
Probability is the frequency of observed frequency from the sample.
For example, when we observed the tail of coin 505 times out of 1000 trials, we can say that the probability of observing the tail of the coin is
To get the probability that can more accurately represent the parameter, we should increase the number of trials as many as possible.
Thus, the definition of probability is a long-term frequency (Frequentist statistics).
We brought this definition just by writing down the number we observed. So it is objective.
There is another definition of probability, which is subjective. If we use the observation as prior knowledge and then calculate the probability, it is subjective. This statistic is called the bayesian statistic.
*Definition of Probability
Obsective: frequentist statistics / Subsective: Baysian statistic
Let's define probability in terms of set. Population can refer as {set}. {set} means all the values for the population. In the sample, we can use the concept of the set too. Sample space (S) means a set of all the results, which can be obtained by sampling.
For example, we can say that...
The sample space for number of dice when we toss dice: S = {1,2,3,4,5,6}
In the Sample space (S) = {e1, ..., eN(N=total number of elements)}, the probability of event A which consist of the number of m is P(A) =
