A classic question of logic is: Which came first, the chicken or the egg? We mig

Question

A classic question of logic is: Which came first, the chicken or the egg? We might adapt that question for exploring the various probability distributions. Many things we analyze can be best understood as manifestations in the world of the probabilities these distributions describe. Knowing the appropriate descriptive distribution allows us to make predictions about what has happened, or will happen, in the world.

Discuss how you would explain to a manager why, when, and how you would make use of these distributions in order to solve a problem or address an opportunity. What would you need to start, and what you have after your analysis?

Explanation / Answer

Any situation ( an event in statistical/probabilistic language ) is a manifestation of some causes acting together. To understand a situation under our study there is only one way is to observe it ( in a scientific way i.e, through measurements ) in a qualitative or quantitative way. Qualitative data cannot give much effective way to interpret the situation so quantification is anyhow done. These quantified measurements are our raw data obtained. But this raw data is can be thought of as only an instance from a pool of several others (which we may experience from the multiple occurrences of the same event or can be conceptually visualized). That pool of several values and their occurrences are our prime interest since we want to know the outcome ( values ) of that event apriori so that we can use it for our purpose. To interpret the occurrences of different values at different instances we assign some causes logically which may influence the event. Then we propose or introduce some model relating the outcome variable and the causing variables. But every model is an approximation to the reality even if we consider a big model. This error due to approximation needs some treatment and there we introduce the chance factor ( since the notion of error is such that it cannot be assigned to any causes) or the probability distribution that governs the occurrence of the error. Sometimes we are sure of the structure of the rule of occurrence but not the actual one sometimes nothing is known, and thus we need to estimate ( first one is parametric, later one is nonparametric) it through the observed data after ignoring the definite causes.

Steps are as follows in short:

1) to identify the study variable in which we are interested

2) Identify the causes related to the study variable and quantify them as well.

3) propose a model and structure of the error.

4) estimate the nature of the rule through some optimal procedure.

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