Let X sim B(n, p). If E(X)=5 and operatorname | vedclass

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

Question

(B) Given that $X$ follows a binomial distribution $B(n, p)$.For a binomial distribution,the mean $E(X) = np = 5$ and the variance $\operatorname{Var}

Vedclass · Accepted Answer

$\left(\frac{1}{2}\right)^{10}$

Vedclass · Answer

(B) Given that $X$ follows a binomial distribution $B(n, p)$.For a binomial distribution,the mean $E(X) = np = 5$ and the variance $\operatorname{Var}(X) = npq = 2.5$.Dividing the variance by the mean,we get $q = \frac{npq}{np} = \frac{2.5}{5} = 0.5 = \frac{1}{2}$.Since $p + q = 1$,we have $p = 1 - 0.5 = 0.5 = \frac{1}{2}$.Substituting $p = \frac{1}{2}$ into $np = 5$,we get $n 	imes \frac{1}{2} = 5$,which implies $n = 10$.We need to find $P(X The probability mass function is given by $P(X = k) = {}^{n}C_{k} p^{k} q^{n-k}$.For $k = 0$,$P(X = 0) = {}^{10}C_{0} \left(\frac{1}{2}ight)^{0} \left(\frac{1}{2}ight)^{10-0} = 1 	imes 1 	imes \left(\frac{1}{2}ight)^{10} = \left(\frac{1}{2}ight)^{10}$.

Let $X \sim B(n, p)$. If $E(X)=5$ and $\operatorname{Var}(X)=2.5$,then find $P(X < 1)$.

Similar Questions

$A$ coin is tossed $10$ times. The probability of getting exactly six heads is

On a multiple choice examination with three possible answers for each of the five questions,what is the probability that a candidate would get four or more correct answers just by guessing?

$8$ coins are tossed simultaneously. The probability of getting at least $6$ heads is

$A$ bag contains $2$ white and $4$ black balls. $A$ ball is drawn $5$ times with replacement. The probability that at least $4$ of the balls drawn are white is

In a binomial distribution,the probability of success is $\frac{1}{4}$ and the standard deviation is $3$. Then,its mean is

Vedclass Test Series

Exam Paper Generator

Online Exam Module