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If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X= 4) in terms of α.
Given:
P (X = 1) = P (X = 2) = α
P (X= 4)=?
P(x=r)= nCr pr qn-r
P(x=1)= nC1 p1 qn-1
=np
qn-1 (1)
P(x=2)= nC2 p2 qn-2
(2)
Equating both equations ,we have:
2q = (n-1) p
4q2 = (n-1)2 p2
P(x=4)= nC4 p4 qn-4
For large n; n
0
So,