THEORETICAL PROBABILITY DISTRIBUTIONSIn day to day life, we come across many random variables such as ------1.Number of male children in a family having three children.2.Number of passengers getting into a bus at the bys stand .3.I.Q. of children4.Number of stones thrown successively at a mango on the tree until themango in hit5.Marks scored by a candidate in the P.U.E. examination. For a quick analysis of distributions of such random variables, weconsider their theoretical equivalents. These equivalent distributions areoriginated according to certain theoretical assumptions and restrictions.Such theoretically designed distributions are called theoreticaldistributions.
• There are many types (families) of theoretical distributions. Some of them• (i) Bernoulli distribution• (ii) Binomial distribution• (iii) Poisson distribution• (iv) Hypergeometric distribution• (v) Normal distribution.• The Bernoulli distribution and the Binomial distribution were discovered by James Bernoulli during the first decade of eighteenth century. These works were published posthumously in 1713.• The Poisson distribution was introduced by S.D. Poisson in 1837.• The Normal distribution was introduced by De Moivre in 1753. This distribution is also called Gaussian distribution.
What Does the Binomial Distribution Describe?• The probability of getting all “tails” if you throw a coin three times• The probability of getting four “2s” if you roll six dice• The probability of getting all male puppies in a litter of 8• The probability of getting two defective batteries in a package of six
Uses of the Binomial Distribution• Quality assurance• Genetics• Experimental design
The Statistics……..• If you face 45 shots and allowed 5 goals, your save percentage is .888• So P(S)=88%• And P(F)=12%
The Problem…………• What is the probability of saving(P(S)) 70 out of 90 shots?Probability of Success=• P(S)= 78%Probability of Failure=• P(F)=22%
BINOMIAL DISTRIBUTION• A Probability distribution which has the following probability mass function (p.m.f) is called Binomial distribution.