NIMCET 2017 — Mathematics PYQ

Concept:

The binomial distribution of a random variable X is given by,

$P(X=k)={}^n{C}_k{p}^k{q}^{n-k}$  

$\text{Mean}=np$  

$\text{Variance}=npq$  

Calculation 

\text{Given, the mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively,}  

$\Rightarrow \text{mean}=np=4....(1)$  

$\Rightarrow \text{variance}=npq=2....(2)$  

\text{From equation (1) and (2), we have}  

$\Rightarrow q=\frac{1}{2}$  

\text{We know, } $p=1-q$  

$\Rightarrow p=\frac{1}{2}$  

\text{From equation (1), we have}  

$n=8$  

\text{The binomial distribution of a random variable X is given by,}  

$P(X=k)={}^n{C}_k{p}^k{q}^{n-k}$  

$P(X=1)={}^8{C}_1{p}^1{q}^{8-1}$  

$\Rightarrow P(X=1)=8\cdot \frac{1}{2}\cdot \frac{1}{2^7}$  

$\Rightarrow P(X=1)=\frac{1}{32}$