Find the binomial probability distribution wh | 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 $E(X) = np = 3$ and the variance is given by $Var(X) = npq = 2$. Dividing the variance by the mea

Vedclass · Accepted Answer

$\left(\frac{2}{3}+\frac{1}{3}\right)^9$

Vedclass · Answer

(A) For a binomial distribution,the mean is given by $E(X) = np = 3$ and the variance is given by $Var(X) = npq = 2$. Dividing the variance by the mean,we get $\frac{npq}{np} = \frac{2}{3}$,which implies $q = \frac{2}{3}$. Since $p + q = 1$,we have $p = 1 - q = 1 - \frac{2}{3} = \frac{1}{3}$. Substituting $p = \frac{1}{3}$ into $np = 3$,we get $n 	imes \frac{1}{3} = 3$,which implies $n = 9$. The binomial distribution is given by $(q + p)^n = \left(\frac{2}{3} + \frac{1}{3}ight)^9$.

Find the binomial probability distribution whose mean is $3$ and variance is $2$.

Similar Questions

The probability of getting a success in a trial is five times that of a failure. The probability of getting at most one success in $5$ trials is:

The mean and variance of a random variable $X$ having a binomial distribution are $6$ and $3$ respectively. The probability of variable $X$ less than $2$ is . . . . . . .

$A$ fair coin is tossed $100$ times. The probability of getting a head an even number of times is

If five dice are thrown simultaneously,then the probability that at least three of them show the same numbered face is

Four fair dice are thrown independently $27$ times. Then the expected number of times,at least two dice show up a three or a five,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module