Introduction ( Math T )

Introduction

Binomial distribution is is invented by Jacob Bernuolli. Bernuolli. The binomial distribution distribution model is an impo import rtan antt prob probab abil ilit ity y mode modell that that is used used when when ther there e are are two two possi possibl ble e outcomes (hence "binomial"). For example, children with a bacterial infection miht respond to antibiotic therapy or not, medical device such as a coronary stent miht be successfully successfully implanted or not. These are !ust a few examples examples of applications applications or proce processe sses s in which which the outcom outcome e of inter interest est has two possible possible values. values. The two outcom outcomes es are are often often labele labeled d "succe "success" ss" and "fail "failure ure"" with with succes success s indica indicatin tin  the presence of the outcome of interest. n proba probabil bility ity theory theory and statis statistic tic,, #oisson oisson distri distribut bution ion is named named after after a French rench mathematician name $im%on &enis #oisson, it is a discrete distribution that express the probability of a iven number of events occurrin in a 'xed amount of time. #oisson distribution applies when the occurrences are independent, so that one event will not diminishes or increases the chance of another event. The #oisson distribution can also be used for the number of events in other speci'ed intervals such as distance, area or volume.  The normal distribution is an important and most widely used distribution in statistics. t is sometimes called the "bell curve," althouh the tonal ualities of such a bell would be less than pleasin. t is also called the "aussian curve" after the mathematician *arl Friedrich auss.  The normal distribution is remar+ably useful becaus because e of the centra centrall limit theor theorem em.. n its its most most ene enera rall for form, it stat states es that that averaes of random variables independently variables  independently drawn from independent distributions are normally distributed.  The aim of this pro!ect is to determine the relationship between binomial, poisson and normal distribution. Binomial distribution may be approximated, under certain cir circumst cumstan ance ces s by pois poisso son n dist distri ribu buti tion on or norm normal al dist distri ribu buti tion on.. ne ne prac practi tica call advantae is that the calculation is much less tedious to perform.