Mark the correct alternative in the following: For a binomial variate X, if n = 3 and P (X = 1) = 8 P(X = 3), then p =

Question

Philoid · Accepted Answer

Given:

n=3

P (X = 1) = 8 P (X = 3)

P =?

P(x=r)= ⁿC_r p^r q^n-r

P(x=1)= ⁿC₁ p¹ q^n-1

=3pq^{2 (1)}

P(x=3)= ³C₃ p³ q⁰

= p³⁽²⁾

Put values in the equations ,we have:

3pq² =8 p³

3 (1-p)² = 8p²

3+3p²-6p = 6p²

5p²+6p-3=0