Salta al contenuto

Conditional frequency

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

Rispondi

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