Poisson Distribution for Statistical Analysis
"Learn about Poisson distribution, a discrete probability distribution used in various fields like business statistics, biology, insurance, and quality control. Discover its history, formula, uses, and properties for practical applications."
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Presentation Transcript
POISSON DISTRIBUTION CLASS : CLASS : - - M.COM [PREVIOUS] (2 M.COM [PREVIOUS] (2ND SUBJECT : SUBJECT :- - BUSINESS STATISTICS BUSINESS STATISTICS DEPT. : DEPT. :- - DEPT. OF COMMERCE AND DEPT. OF COMMERCE AND MANAGEMENT MANAGEMENT COLLEGE : COLLEGE :- - I.B. (PG) COLLEGE, PANIPAT I.B. (PG) COLLEGE, PANIPAT BY: BY:- - PROF. VANITA REHANI PROF. VANITA REHANI NDSEM SEM ) )
WHAT IS POISSION DISTRIBUTION ? Poisson distribution is a discrete probability distribution and it is a limiting form of the binomial distribution in which n, the number of trials ,becomes very large & p, the probability of success of the event is very small.
HISTORY : The distribution was first introduced by Sim on Denis Poisson and published, together with his probability theory, in 1837. A practical application of this distribution was made by Ladislaus Bortkiewicz in 1898 when he was given the task of investigating the number of soldiers in the Prussian army killed accidentally by horse kick.
FORMULA OF POISSON DISTRIBUTION: Where, P(X=x)=prob. of obtaining x no. of success, M=np=parameter of the distribution E=2.7183(base of natural logarithms)
USES OF POISSON DISTRIBUTION: To count the number of phone calls received at an exchange in an hour; To count the number of customers arriving at a toll booth per day; In Biology to count the number of bacteria; In Insurance to count the number of casualities; In statistical quality control to count the number of defects of an item;
CONTINUED To count the number of defective blades in a lot of manufactured blades in a factory; To count the number of deaths at a particular crossing in a town as a result of road accident; To count no of suicides committed by lovers point in a year; To count the number of typing errors per page in a typed material;
PROPERTIES OF POISSON DISTRIBUTION: Poisson Distribution is a discrete probability distribution; Used in those situation where, p 0 and q 1; It has only one parameter m and m=np The constants of Poisson Distribution are: Mean=m=np Variance= =m S.D= = M
CONTINUED In Poisson Distribution, MEAN=VARIANCE; Poisson Distribution is always positively skewed but skewness diminishes as the value of m increases;
PROBLEM: Q: The number of flaws in a fibre optic cable follows a Poisson distribution. The average number of flaws in 50m of cable is 1.2. (i) What is the probability of exactly three flaws in 150m of cable? (ii) What is the probability of at least two flaws in 100m of cable? (iii) What is the probability of exactly one aw in the first 50m of cable and exactly one aw in the second 50m of cable?
THANK YOU HAVE A NICE DAY
