Hidden tiger (1): Conditional, prior and joint probability tables; problem description

Antonio Sala, UPV

Difficulty: * ,       Relevance: ,      Duration: 22:26

*Enlace a Spanish version

Summary:

This video is the first of a case study of a “hidden tiger” problem that will allow us to review and improve the understanding of many concepts in Statistics and probability.

In this first video, the problem is outlined: we have a tiger that is in one of two cages (left or right), but whose roars are sometimes heard by a zookeeper from the wrong side because the tiger roars towards a passageway connecting the doors. The final goal of the problem is to find out where the tiger is (to “save the zookeeper’s life” by leaving through the other door)... but for that, you have to understand many previous concepts... starting with the “probability tables” we are introducing here.

Here we explain conditional probability tables, of “observations” (hearing roars left or right) conditioned on ‘location” of the tiger (tiger left or right).

After that, we define the concept of “a priori” probability that the tiger is on one side or the other before hearing the first roar, and with this we calculate the joint probability $p(m\wedge t)=p(m|t)\cdot p(t)$ of the four possible “atomic” combinations of “roar hearing” and “tiger location”.

The video discusses the interpretation and relationships between these probability tables. Specifically, although everything can be calculated from the “joint” table, a continuation of this one), it turns out that dividing the problem into subproblems is conceptually simpler with the concept of conditional probability ( we’ll delve further into these issues in the video [tiger2EN]).

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.