If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9 P(X = 3), then find the value of p.

Question

Philoid · Accepted Answer

Given:

n=5

p(x=2)=9p(x=3)

p=?

P(x=r)= ⁿC_r p^r q^n-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