Suppose X has a binomial distribution B (6, 1/2 ) show that X = 3 is the most likely outcome. 10) In a binomial distribution, the sum of mean and variance is 42. Product is 360. FInd the distribution.

X is the random variable whose binomial distributionis.

Therefore,n= 6 and

It can be seen that P(X =x) will be maximum, ifwill be maximum.

The value ofis maximum. Therefore, forx= 3, P(X = x) is maximum.

Thus, X = 3 is the most likely outcome

2)in a binomial distribution mean=np,variance=npq

given np+npq=42 and n²p²q=360

solving above 2 equations we get p=3/5,q=2/5 and n=50

so binomial distribution is (3/5+2/5)⁵⁰

Thanks and Regards

Shaik Aasif

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