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# BINOMIAL DISTRIBUTION -anchu J S (1).pptx

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Binomial distribution
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# BINOMIAL DISTRIBUTION -anchu J S (1).pptx

Binomial distribution
Introduction
Definition
Success ans failure
Formula
Example
Nc

Binomial distribution
Introduction
Definition
Success ans failure
Formula
Example
Nc

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### BINOMIAL DISTRIBUTION -anchu J S (1).pptx

1. 1. SUBMITTED BY ANCHU J S 72O822208009 MBA BINOMIAL DISTRIBUTION
2. 2. INTRODUCTION  The binomial distribution is also known as Bernoulli distribution.  This theory is propounded by Swiss Mathematician a ‘James bernouli’ in 1685.  It is a process through which one can arrive the result of the experiment mainly success or failure
3. 3. DEFINITION In probability theory and statistics ,the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments , each asking a yes –no question ,and each with its own Boolean – valued outcome :SUCCESS OR
4. 4. FORMULA P(x) = nCx px (q)n-x WHERE, P = Binomial probability X = number of times for a specific outcome within n trails nCx = number of combinations p = probability of success on a single trial q = probability of failure on a single trial n = number of trials
5. 5. SUCCESS AND FAILURE Consider an event associated to a random experiment . when the random experiment is repeated a number of times ,the event may or may not occur in each of those experiments . the occurance of the event may be named as “success” and non-occurance , “failure” Therefore Random experiments has only two possible outcomes “success” and “failure”.
6. 6. for example,  In throwing a die, “we can say getting six” and “not getting six” are two events. One is success and other is failure
7. 7. SITUATIONSWHEREBINOMIALDISTRIBUTIONCAN BEAPPLIED Random experiment has only two events(success and failure) Trails are independent The experiment is repeated the finite number of times. Probability for a success in a single trial remains constant from trial to trial of the experiment.
8. 8. Propertiesofbinomialdistribution  Binomial distribution is discrete probability distribution  The shape and location of binomial distribution changes as ’p’ changes for a given ‘n’.  Binomial distribution has mean= np  Standard deviation =√(npq)  Mean of the binomial distribution changes as ‘p’ changes for a given ‘n’.
9. 9. examples The probability that a person can achieve a target is 3/4.The count of tries is 5. What is the probability that he will attain the target at least thrice? Solution: Given that, p = ¾, q = ¼, n = 5. Using binomial distribution formula, we get P(X= x) = nCx .px (q)n-x Thus, the required probability is: P(X = 3) + P(X=4) + P(X=5) = 5C3 · (¾)3 (¼ )2 + 5C4 · (¾)4 (¼ )1 +5C5 · (¾)5 = 459/512. Therefore, the probability that the person will attain the target atleast thrice is 459/512.