## Request

- Understand and discuss the notion of conditional frequency
- Insight 2: Research the various approaches to
define the concept of probability, the ‘Kolmogorov axioms’ and the relationship with the notion of (relative) frequency. - Exercise: take a CSV file and read all the lines. Split each line by using the ‘stringsplit method and (if you can) load the data as properties of suitable objects in a list of objects (example object student)

## Execution

To introduce the concept of conditional frequency, we must discuss the concept of conditional probability. For example, I have two honest dice and

S = {(i,j), i = 1,2,3,4,5,6 , i = 1,2,3,4,5,6}

defining *i* is the result of the first dice and *j* is the result of the second one. Since the dice are honest every combination of *(i,j)* has the probability of 1/36 to happen. We suppose now that the first dice results, 3, so we fix *i* = 3 and we ask ourself: What is the probability that the sum of the results will be 8? By fixing *i* as 3 there are 6 other possibles results : (3,1), (3,2), (3,3), (3,4), (3,5), (3,6) . This means that if *i = 3* the probability of the above events to happen is 1/6 and the probability of the other 30 initial events is 0. Then we can conclude that the probability of *i+j = 8* when* i = 3* is just 1/6. If we now call the event *“sum of *i* + j = 8″* **E** and the event *“i = 3”* **F**, then we define what’ve just calculated as the conditional probability of **E** given **F** and we denote that in this way:

P(E|F)

We can also say that if **F** is verified, to verify **E**, the event must be part of the **E AND F** (where AND is the intersection). Since now **F** is an event really happened it will become the new set of possibles solutions. So the conditional probability is the division of the probability of** E AND F** to the probability of **F**:

P(E|F) = P(E AND F) / P(F)

Given these definitions, the conditional frequency is the number of occurrences of the event **E** given the event **F** and it has the same formula the conditional probability.

## Insights

Research the various approaches to define the concept of probability, the ‘Kolmogorov axioms’ and the relationship with the notion of (relative) frequency.

## Sii il primo a commentare