Salta al contenuto

## 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 i want to describe all the possibles results I can use this notation:

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.

Published inStatistics

## Sii il primo a commentare

Questo sito usa Akismet per ridurre lo spam. Scopri come i tuoi dati vengono elaborati.