CSCI A113
Lecture Notes Seven
Fall 2001
| |
CSCI A113
|
Check the notes from Nov. 1 (Four) for a review of Probability.
Probabilty can be approached in two ways:
A priori means that which can be deduced from reason alone, without experience.
From this point of view probability is defined as
A posteriori means "after the fact", and in the context of probability it means after some data have been collected. From this point of view the definition is:
To determine the probability of a 2 (two) in one roll of one die using the empirical approach, we would have to take the actual die, roll it many times, and count the number of times a 2 (two) has occurred.
The more times we roll the die, the better.
Let's assume (for the sake of the example) that we roll the die 100,000 times and that a 2 (two) two occurs 16,000 times. The probability of a two occuring in one roll of the die is 0.16 (16,000 divided by 100,000). This is also the a priori probability, calculated as 1/6.
Note that, with this approach, it is necessary to have the actual die and to collect some data before determining the probability. But that's what we will do for the midterm. In this class we measure, collect data, summarize, analyze, and report our findings.
Take a look at the notes from Oct 25 (Two) for a review of the type of frequency distributions we have studied. After a bit of thinking it should be obvious that empirical probability is a relative frequency:
(That's the frequency of occurrence of ei divided by the total number of cases).
The certain event has probability 1 and is basically composed of all possible outcomes.
Thus, for the midterm, and in our simulations, we will calculate relative frequencies and cumulative relative frequencies as in the lab manual chapter 7, only with histograms.
The next set of lecture notes will give you an idea of what the midterm will look like.
A113