Q10 of 99 Page 33

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


=npqn-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,


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