Random Variable

• The value of random variable varies from trial to trial.
• The outcome of an experiment need not be a number
  e.g. the outcome when a coin is tossed can be 'heads' or 'tails'.

• Discrete R. V.: E.g., a coin is tossed ten times. The random variable X is the number of tails that are noted.

• Continuous R. V.: E.g., light bulb is burned until it burns out. The random variable Y is its lifetime in hours.

• A random variable has either an associated probability distribution (aka probability mass function, discrete random variable) or probability density function (continuous random variable).

Probability mass/density function

This function determines the shape/distribution of R.V.

Let's define that the R.V. X is the number of heads after a single biased-coin flip:
X=0 for tail
X=1 for head

Then the probability mass function $f(k) = Prob[X=k]$ ($k$=0,1) with $f(0) = 1-p$ and $f(1) = p$. (This is called Bernoulli distribution)