Question

If the difference of mean and variance of a binomial distribution \(B(n,p)\) is \(\dfrac{4}{7}\) and their product is \(\dfrac{20}{7}\), then \(P(X=1)=\)

• A. \(\left(\dfrac57\right)^6\)
• B. \(2\left(\dfrac57\right)^6\)
• C. \(2\left(\dfrac34\right)^6\)
• D. \(\left(\dfrac34\right)^6\)

Hint:

For a binomial distribution, \[ \boxed{\mu=np,\qquad \sigma^2=npq.} \] Also, \[ \boxed{P(X=r)={n\choose r}p^rq^{\,n-r}.} \]

Answer 1

The Correct Option is B