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

Question

A classic question of logic is: Which came first, the chicken or the egg? In this class, we might adapt that question for exploring the various probability distributions we’ve seen this week and last week. Many things we analyze as engineers 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 non-engineering 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?

A classic question of logic is: Which came first, the chicken or the egg? In this class, we might adapt that question for exploring the various probability distributions we’ve seen this week and last week. Many things we analyze as engineers 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 non-engineering 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

WHY use probability distributions : There are many phenomenon occuring in the real world, for which it is extremely difficult to have a precise methematical model derived from the basic first principles scientific laws. However, we not only need to analyze such phenomenon under the realm of engineering analysis but also wish to make predictions of future states of the world. In the absence of any first principles based model, we must take an alternative approach of enumerating exhaustively all the possibilities and quanitfying the likelihood of occurence of each, in order to make business profitable. Therefore we need to make use of these probability distributions.

WHEN use Probability distributions : We can use probability distributions approach when we don't have an existing first principle based model to describe the phenomenon under consideration BUT we do have a finite set (preferably a sufficiently large one) of input - output observations generated by that phenomenon.

HOW to use these distributions : We would start with a predefined probability distribution model (Parametric model) which relate the input to output. Then we will use the available input- output data obtained from the phenomenon, in order to estimate the parameters of the chosen parametric probability distribution. Once we have estimated the parameters, we can describe quantitatively as to which ouput value is most likely to occur if input is of certain value and which are less likely to occur. Such quantification can help take business decisions with the profit kept in mind.

At the start, we will require (1) sufficient data relating input to output of the phenomenon under consideration. and (2) An assumed parametric model of probability distribution which we believe, can accurately describe the phenomenon.

After our analysis, we will have fully estimated probability distribution, which we can use to describe which output values are most likely to occur if input values fall within certain range.

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