Properties of Probability Density Functions

The physical processes we study in this text are modeled using models including stochastic terms. Direct numerical simulations based on such stochastic models give results that are hard to interpret and it is therefore common to run many simulations and compute the average, and we have also seen that we can derive models governing the probability density functions. These are powerful tools that provide insight in the processes. In this chapter we will see that it is useful to have specific numbers that characterize stochastic variables and associated probability density functions. We encountered the equilibrium probability of being in the open or closed state (see, e.g., page 57) and we introduced probability density functions (see, e.g., page 30). Here we shall derive some specific (and common) characteristics of the probability density functions and discuss how these characteristics can be used to gain an understanding of calcium release. We will also show how the characteristics relate to the concepts already introduced and we will discuss how the characteristics vary as functions of the mutation severity index. Finally, we will show how the statistical characterizations can be used to evaluate the properties of theoretical drugs.