Python Programming for Biology: Bioinformatics and Beyond

Random variables

Random  variables  describe  numeric  values  that  relate  to  the  outcomes  of  a  random,

probabilistic  process.  A  very  simple  example  of  a  random  variable  is  the  height  of

individual people in a population. A random variable describes a range of possible values,

which  we  call  a  distribution,  and  we  associate  a  probability  with  each  value.  A  random

variable can be applied to discrete events, like counting the number of G:C nucleotides in

a  DNA  sequence,  where  the  number  of  outcomes  is  finite.

5

 Alternatively  the  random

variable  may  be  continuous,  as  is  the  case  with  our  height  example.  However,  in  this

chapter we will  concentrate on discrete  random variables. We  have implicitly  mentioned

random variables earlier in this chapter, in relation to what the sequence separation would

be for the HindIII restriction enzyme cut site. In this case the random variable represents

the  variation  in  the  length  of  the  DNA  sequence  before  the  cut  site,  which  might  be  the

separation  between  one  cut  site  and  another  when  cutting  a  whole  genome  into  small

fragments.  Here  the  distribution  of  lengths,  and  thus  the  probability  of  each,  can  be

modelled  with  the  geometric  distribution,  as  we  describe  below.  By  matching  a  random

variable  to  a  well-characterised  probability  distribution  we  say  something  about  the

---

process  that  generated  it.  Going  further,  if  we  have  a  candidate  model  for  a  random

process  that  matches  the  distribution  (and  thus  explains  our  data)  we  can  then  look  for

deviation from the model. This may suggest a better model or illustrate in what way our

data is not random, e.g. if a restriction enzyme cuts at sites that don’t match expectations.

Next  we  will  go  through  some  of  the  more  commonly  used  probability  distributions.

We aim to give an idea of how they arise and thus what they may be useful for. Practical

biological examples are given in Python, often by making use of the SciPy library, which

has a module for probability and statistics, scipy.stats.