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If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9 P(X = 3), then find the value of p.
Given:
n=5
p(x=2)=9p(x=3)
p=?
P(x=r)= nCr pr qn-r
P(x=1)= 5C1 p1 q4
= 5p q4
P(x=3)= 5C3 p3 q2
= 20 p3 q2
Put values in equation, we have:
5p q4= 9(20 p3 q2)
q2= 9(4 p2)
(1-p)2= 36p2
1+p2-2p= 36p2
35p2+2p-1=0