Probability and Statistics: Theory and Exercises

Accidental events in chemical and process industries may have catastrophic consequences. The present chapter aims to discuss the hazards and risks in chemical and process industries, where chemical species are used and/or transformed. After defining the concept of chemical risk, the possible accidental events in the process industry are presented based on their probability of occurrence. Some examples of relevant chemical accidents that occurred in the past are thoroughly discussed further. Safety measures (i.e., preventive and protective procedures) in safety and process industries and primary and secondary reactions are also described. Finally, a screening method capable of providing a hazard evaluation by calculating the power released during the thermal decomposition of a substance (i.e., the CHETAH method) is presented. 

In this chapter, the basic definitions of probability theory are presented. The logic of presenting the results as events and their quantification, in order to know those that are highly probable or the reverse, are all detailed. It should be noted that in this chapter, we are only interested in knowing how to determine the value of the probability for a single random experiment. 

This chapter presents in detail the calculation techniques for random experiments with a high number of outcomes that are generally impossible to calculate classically. The outcomes can be the number of favorable cases or that of possible ones, necessary to calculate the probability value. It is enough to imagine the situation well, to know which law should be used.

After learning how to determine the probability value for a single random experiment, this chapter gives you the tools for compound random experiments. The probability tree that graphically presents the experiment is defined first, followed by numerous details and laws, leading to the mastery of calculation tricks for an experiment composed of n sub-experiments. 

After the great progress in the theory of probability as a science, the passage towards more flexible and representative definitions and the possibility to be implemented numerically gave the need for a new formulation. From there, the random variable came into existence. Although random problems can be of different kinds, the random variable can be discrete or continuous, qualitative or quantitative. This chapter is dedicated to its extended definition and its exploitation in a simplified way.

In this last chapter of the probability part, the laws of probability are presented. These laws are very important even in statistics. They govern difficult phenomena by simple mathematical formulas, obtained after a few developments. The mastery of these laws will allow the classification of the phenomena by the amounts of the probabilities and the number of elements in the samples (or the population).

The Statistical part was included in only one chapter given the ample details provided for the probability part. For this, the necessary terminology in statistics is presented well as it should be. Thereafter, the exploitation of the central tendency to determine the confidence interval and the risk of error according to different situations are presented in detail and with illustrative examples.