Question

Given X ~ B(n, P) 

(i) If n = 10 and p = 0.4, find E(x) and Var(X). 

(ii) If p = 0.6 and E(X) = 6, find n and Var(X).

(iii) If n = 25, E(X) = 10, find p and SD(X). 

(iv) If n = 10, E(X) = 8, find Var(X).

Answer 1

(i) Given: n = 10 and p = 0.4 

∴ q = 1 – p = 1 – 0.4 = 0.6 

∴ E(X) = np = 10(0.4) = 4 

Var(X) = npq = 10(0.4)(0.6) = 2.4 

Hence, E(X) = 4, Var(X) = 2.4.

(ii) Given: p = 0.6, E (X) = 6 

E(X) = np 

6 = n(0.6)

n = 6/0.6 = 10

Now, q = 1 – p = 1 – 0.6 = 0.4

∴ Var(X) = npq = 10(0.6)(0.4) = 2.4 

Hence, n = 10 and Var(X) = 2.4.

(iii) Given: n = 25, E(X) = 10 

E(X) = np 

10 = 25p

(iv) Given: n = 10, E(X) = 8 

E(X) = np 

8 = 10p