Question

Let $X$ be a random variable following Binomial distribution B in($n.p$),where n is the number of independent Bernoulli trials and $p$ is the probability of success. If $E(X)=1$ and $Var(X)=\dfrac{4}{5}$ ,then the values of $n$ and $p$ are

• A. $n=5,p=\dfrac{4}{5}$
• B. $n=1,p=\dfrac{1}{5}$
• C. $n=1,p=1$
• D. $n=5,p=\dfrac{1}{5}$
• E. $n=1,p=\dfrac{4}{5}$

Answer 1

Answer: (D)

$n=5,p=\dfrac{1}{5}$

Answer 2

Give that;

$E(X)=n.p=1$ and $Var(X)=4.5$

We know that,

$Var(X)=n.p(1−p)$

$⇒1-\dfrac{4}{5}=p$

$⇒0.2=p$

$p=0.2=\dfrac{1}{5}$

and

$n=1/0.2=5$

$n=5$

Hence the required $n$ and $p$ are $5$ and $\dfrac{1}{5}$ respectively. (_Ans)