Question

A discrete random variable X is believe to follow a binomial distribution b(x; 5, p). If P(X = 0) = 243/1024, then find P(X = 3).

Answer 1

$$P(X=0)=\dbinom{5}{0}(p)^{0}(1-p)^{5-0}=(1-p)^{5}$$

$$=\dfrac{243}{1024}$$

$$1-p=\dfrac{3}{4}$$

$$p=\dfrac{1}{4}$$

$$P(X=3)=\dbinom{5}{3}(\dfrac{1}{4})^{3}(\dfrac{3}{4})^{5-3}=\dfrac{45}{512}$$