In Binomial distribution, if $E(X)=40 $ and $V(X)=8, $ then value of $P(X=1), $ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{8}{5^{48}}$
In a Binomial Distribution,
Mean = $E(X)=np=40$ [Given] ...(1)
Variance = $V(X)=np(1-p)=8$ [Given] ...(2)
Substituting $np=40$ in equation (2)
$40(1-p)=8$
$1-p=\frac{1}{5}$
$p=\frac{4}{5}$
$⇒n=40×\frac{5}{4}=50$
$P(X+1)={^{50}C}_1(\frac{4}{5})(\frac{1}{5})^{49}$
$=\frac{8}{5^{48}}$