For a binomial distribution,the mean and vari | vedclass

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

Question

(D) For a binomial distribution,the mean is given by $np = 4$ and the variance is given by $npq = 2$. Dividing the variance by the mean,we get $q = \f

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(D) For a binomial distribution,the mean is given by $np = 4$ and the variance is given by $npq = 2$. Dividing the variance by the mean,we get $q = \frac{npq}{np} = \frac{2}{4} = \frac{1}{2}$. Since $p + q = 1$,we have $p = 1 - \frac{1}{2} = \frac{1}{2}$. Substituting $p = \frac{1}{2}$ into $np = 4$,we get $n 	imes \frac{1}{2} = 4$,which implies $n = 8$. The probability mass function for a binomial distribution is $P(X = k) = \binom{n}{k} p^k q^{n-k}$. For $X = 2$,$P(X = 2) = \binom{8}{2} (\frac{1}{2})^2 (\frac{1}{2})^{8-2} = \binom{8}{2} (\frac{1}{2})^8$. Calculating the combination,$\binom{8}{2} = \frac{8 	imes 7}{2 	imes 1} = 28$. Thus,$P(X = 2) = 28 	imes \frac{1}{256} = \frac{28}{256}$.

For a binomial distribution,the mean and variance are $4$ and $2$ respectively. What is the probability of $X = 2$ (in $/256$)?

Similar Questions

The probability that a person who undergoes a bypass surgery will recover is $0.6$. The probability that of the $6$ patients who undergo similar operations,half of them will recover is:

In a Binomial distribution consisting of $5$ independent trials,probabilities of exactly $1$ and $2$ successes are $0.4096$ and $0.2048$ respectively,then the probability of getting exactly $4$ successes is

The number of trials conducted in a binomial distribution is $n = 6$. If the difference between the mean and variance of this variate is $\frac{27}{8}$,then the probability of getting at most $2$ successes is:

When six coins are tossed simultaneously,the probability of getting at least $4$ heads is

$A$ student writes an examination which contains $8$ true or false questions. If he answers $6$ or more questions correctly,he passes the examination. If the student answers all the questions,then the probability that he fails in the examination is

Vedclass Test Series

Exam Paper Generator

Online Exam Module