One of the most elementary and useful discrete random variables is associated with the coin-tossing experiment. In the experiment, either one coin is tossed ‘n’ times or ‘n’ coins are tossed once. The observation ‘head or tail’ is recorded for each toss. Numerous experiments of practical importance in social sciences, physical sciences and industry resemble the coin-tossing experiment.

Properties of Binomial experiment:


  • The experiment consists of n identical trials.
  • Each trial results in one of the two outcomes. For lack of a better nomenclature. One outcome is called success and the other is a failure.
  • The probability of success in a single trial is equal to P and of failure is q = 1 – P.
  • The trials are independent.
  • One is interested in r successes during the n trials.

The two events, success and failure are qualitative in nature.

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Properties of Binomial Distribution:

The binomial distribution has three significant attributes. They are arithmetic mean, standard deviation and pattern or shape of the distribution.

  • The mean of the binomial distribution is Mean = nP
  • The standard deviation of the binomial random variable measures the dispersion of the binomial distribution. The standard deviation is determined by
  • σ = √nPq
  • Pattern or shape of the binomial distribution.


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