Q6 of 99 Page 33

If the mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, find P (X = 1).

Given:

Mean=4

Variance=2

P(x=1)=?

P(x=r)= ⁿC_r p^r q^n-r

P(x=1)= ⁿC₁ pq^n-1

= npq^n-1

np(1-p)=2

4(1-p)=2

np=4

n=8

P(x=1)

If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.

The mean of a binomial distribution is 10 and its standard deviation is 2, write the value of q.

If the mean and variance of a binomial variate X are 2 and 1 respectively, find P(X > 1).