UPSC NDA Math Model Paper 5

Given, the mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively,
⇒ mean = np = 4 ....(1)
⇒ variance = npq = 2 ....(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