VITEEE 2018 Paper

The binomial distribution of a random variable X is given by,
P(X=k)=‌nCkpkqn−k
Mean =np
Variance =npq
Given, the mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively,
⇒mean =np=4
⇒‌ variance ‌=npq=2
From equation (1) and (2), we have
⇒q=‌

1

2

We know, p=1−q
⇒p=‌

1

2

From equation (1), we have
n=8
The binomial distribution of a random variable X is given by,
P(X=k)=‌nCkpkqn−k
⇒P(X=1)=‌8C1p1q8−1
⇒P(X=1)=8⋅‌

1

2

⋅‌

1

27

⇒P(X=1)=‌

1

32