The mean and variance of a binomial distribut | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For a binomial distribution,the mean is given by $\mu = np$ and the variance is given by $\sigma^2 = npq$.Given that the mean is $6$,we have $np =

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(A) For a binomial distribution,the mean is given by $\mu = np$ and the variance is given by $\sigma^2 = npq$.Given that the mean is $6$,we have $np = 6$.Given that the variance is $4$,we have $npq = 4$.Dividing the variance by the mean,we get $\frac{npq}{np} = \frac{4}{6}$,which simplifies to $q = \frac{2}{3}$.Since $p + q = 1$,we have $p = 1 - q = 1 - \frac{2}{3} = \frac{1}{3}$.Substituting the value of $p$ into the mean equation: $n 	imes \frac{1}{3} = 6$.Therefore,$n = 6 	imes 3 = 18$.

The mean and variance of a binomial distribution are $6$ and $4$. The parameter $n$ is

Similar Questions

$A$ die is thrown four times. The probability of getting a perfect square in at least one throw is

$A$ person fails $4$ times in a game when he plays $9$ times. If he plays $15$ times, the probability of having success at most one is

Let a biased coin be tossed $5$ times. If the probability of getting $4$ heads is equal to the probability of getting $5$ heads,then the probability of getting at most two heads is

If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively,then what is the probability that $X \geq 1$?

$A$ pair of fair dice is thrown $4$ times. If getting the same number on both dice is considered as a success,then the probability of exactly two successes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module