If the sum of the mean and variance of B.D. for 5 trails is 1.8, the binomial distribution is
A binomial distribution is characterized by 2 parameters:
n - number of trials
p - probability of success in 1 trial
We already know n=5, we need to find p.
Mean of a binomial distribution is given by
mean =np
Variance is given by
variance =np(1−p)
mean+variance=1.8
5p+5p(1−p)=1.8
5p2–10p+1.8=0
p2−(1.8+0.2)p+0.36=0 [Dividing by 5 then using factor]
(p−0.2)(p−1.8)=0
p=0.2 or p=1.8(non−considerable) because p is probability so it can not be greater than 1.
So the binomial distribution is n=5,p=0.2.