Discussion Forum

Let $X\sim B(n,p),if E(x)=5,Var(X)=2.5,$   then $ p(X<1)$ is equal to 

Answer:

Explanation:

Given  , mean E(X)=5, and variance , Var(X)=2.5

$\therefore$    np=5 and npq=2.5

$\Rightarrow$  5q=2.5 $\Rightarrow$ q=$\frac{1}{2}$

$\Rightarrow$    p+q=1

$\therefore$     $p=1-\frac{1}{2}=\frac{1}{2}$

$\therefore$ np=5                  

$\Rightarrow$  $n\times\frac{1}{2}=5$                 $\left[\because p=\frac{1}{2}\right]$

$\Rightarrow$     n=10

$p(X<1)=p(X=0)=^{n}C_{r}p^{r}q^{n-r}$

= $p(X<1)=p(X=0)=^{10}C_{0}\left(\frac{1}{2}\right)^{0}\left(\frac{1}{2}\right)^{10-0}$

$=1\times1\times\left(\frac{1}{2}\right)^{10}=\left(\frac{1}{2}\right)^{10}$