Binomial distribution

UNIVERSITY SCHOOL OF MANAGEMENTKURUKSHETRA UNIVERSITY

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YATIN BHARDWAJ48MBA (2YR)USM-KUK

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BY : YATIN ROLL NO. 48 MBA(G)

PRESENTATION ON

BINOMIAL DISTRIBUTION

INTRODUCTION

Binomial distribution was given by Swiss mathematician James Bernouli(1654-1705) in 1700 and it was first published in 1713. It is also known as ‘Bernouli Distribution’.



MEANING...

Binomial distribution is a discrete probability distribution which is obtained when the probability p of the happening of an event is same in all the trials, and there are only two events in each trial.



CONTINUE.... E.g... The probability of getting a

head, when a coin is tossed a number of times, must remains same in each toss i.e. P= 1/2



CHARACTERISTICS OF BINOMIAL DISTRIBUTION

It is a discrete distribution which gives the theoretical probabilities.

It depends on the parameter p or q, the probability of success or failure and n(i.e. The number of trials). The parameter n is always a positive integer.

The distribution will be symmetrical if p=q. It is skew symmetric or asymmetric if p is not equal to q.



CONTINUE...

The statistics of the binomial distribution are: Mean=np, Variance=npq, and Standard deviation = npq

The mode of the binomial distribution is equal to that value of x which has longer frequency.



Continue...



Conditions for binomial distribution The random experiment is performed repeatedly a

finite and fixed number of times. The outcome of the random experiment(trials)

results in the dichotomous classification of events. All the trials are independent. The probability of success in any trial is p and is

constant for each trial. q= 1-p is then termed as the probability of failure and is constant for each trial.



E.g... If we toss a fair coin n times(which is fixed and finite), then the

outcome of any trial is one of the mutually exclusive events, viz, head(success) and tail(failure). Further, all the trials are independent, since the result of any throw of coin does not affect and is not affected by the result of other throws.



Ques. Ten unbiased coins are tossed simultaneously. Find the probability of obtaining,

(i) Exactly 6 heads(ii) At least 8 heads(iii) No head(iv) At least one head(v) Not more than three heads(vi) At least 4 heads



Data & Analytics

Binomial distribution