If the mean and variance of a binomial variat | vedclass

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

Question

(C) For a binomial distribution,the mean is given by $np = \frac{4}{3}$  $(i)$ and the variance is given by $npq = \frac{8}{9}$  $(ii)$.Dividing equat

Vedclass · Accepted Answer

$\frac{8}{27}$

Vedclass · Answer

(C) For a binomial distribution,the mean is given by $np = \frac{4}{3}$  $(i)$ and the variance is given by $npq = \frac{8}{9}$  $(ii)$.Dividing equation $(ii)$ by equation $(i)$,we get:$\frac{npq}{np} = \frac{8/9}{4/3} \implies q = \frac{8}{9} 	imes \frac{3}{4} = \frac{2}{3}$.Since $p + q = 1$,we have $p = 1 - q = 1 - \frac{2}{3} = \frac{1}{3}$.Substituting $p = \frac{1}{3}$ into equation $(i)$:$n 	imes \frac{1}{3} = \frac{4}{3} \implies n = 4$.The probability mass function for a binomial distribution is $P(X=k) = {}^nC_k p^k q^{n-k}$.For $k=2$,$P(X=2) = {}^4C_2 	imes (\frac{1}{3})^2 	imes (\frac{2}{3})^{4-2}$.$P(X=2) = 6 	imes \frac{1}{9} 	imes \frac{4}{9} = \frac{24}{81} = \frac{8}{27}$.

If the mean and variance of a binomial variate $X$ are $\frac{4}{3}$ and $\frac{8}{9}$ respectively,then $P(X=2)=$

Similar Questions

For a binomial distribution,the mean and variance are $6$ and $4$ respectively. Find the value of $n$.

If $A$ and $B$ simultaneously toss one coin each,$50$ times,then the probability of not getting a tail on both the coins in any single toss is:

If $X \sim B(n, p)$ with $n = 10, p = 0.4$,then $E(X^2) =$

It is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If $6$ new cases are reported,then the probability that at least $5$ of them will be solved is

An irregular six-faced die is thrown. The probability that in $5$ throws it will give $3$ even numbers is twice the probability that it will give $2$ even numbers. The number of times,in $6804$ sets of $5$ throws,you expect to get no even number is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module