Question

In a binomial distribution with the parameters n = 3 and P, the second and the third frequency terms are 16 and 15 respectively. Find P.

Answer 1

Given: Frequency term:

T_x = P(x)N 

∴ First frequency term: 

T₁ = P(x = 1) N = 16 

i.e., ³C₁ P₁ q^3-1N = 16 

3P q² N = 16 …………(1) 

Similarity second frequency terms:

 T² = P(x = 2) N = 15 

i.e., ³C₂ P² q^3-2 N = 15 3P²q

N = 15 ………… (2) 

(2) → (1)

P = 0.9375 q; 

∵ q = 1 – P. 

P = (1-P) 0.9375; 

P = 09375 – 0.9375 P 

P + 0.9375 P = 0.9375 

1.9375 P = 0.9375

\(\frac{0.9375}{1.9375}\) = 04838.