Question

If X is a binomial random variable, compute P(X=x) for each of the following cases:

(a) n=3,p=0.15,x=2
(b) n=4,p=0.5,x=1
(c) n=5,p=0.2,x=1
(d) n=4,p=0.1,x=4

Answer 1

(a) $\mathbb P(X=2)=\dbinom320.15^2(1-0.15)^{3-2}=\dfrac{459}{8000}\approx0.0574$

(b) $\mathbb P(X=1)=\dbinom410.5^1(1-0.5)^{4-1}=\dfrac14=0.25$

(c) $\mathbb P(X=1)=\dbinom510.2^1(1-0.2)^{5-1}=\dfrac{256}{625}=0.4096$

(d) $\mathbb P(X=4)=\dbinom440.1^4=\dfrac1{10000}=0.0001$