Question

variance of binomial distribution is 3/4 and probability of failure is 3/4 then state the value of mean​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{Variance\;of\;binomial\;distribution\;is\;\dfrac{3}{4}}$

$\mathsf{and\;probability\;of\;failure\;is\dfrac{3}{4}}$

$\underline{\textbf{To find:}}$

$\textsf{Mean of binomial distruibution}$

$\underline{\textbf{Solution:}}$

$\mathsf{Variance=\dfrac{3}{4}}$

$\implies\mathsf{n\,p\,q=\dfrac{3}{4}}$--------(1)

$\mathsf{Probability\;of\;failure=\dfrac{3}{4}}$

$\implies\mathsf{q=\dfrac{3}{4}}$-----------(2)

$\textsf{Using (2) in (1), we get}$

$\implies\mathsf{n\,p\left(\dfrac{3}{4}\right)=\dfrac{3}{4}}$

$\implies\mathsf{n\,p=1}$

$\implies\boxed{\boxed{\mathsf{Mean=1}}}$

$\underline{\textbf{Formula used:}}$

$\boxed{\begin{minipage}{5cm} \\\\\textbf{In a binomial distribution,}\\\\\mathsf{Mean=np}\\\\\mathsf{Variance=npq}\\\\\textsf{Here,\;n-number\;of\;trials}\\\\\textsf{p-probability of success}\\\\\textsf{q-probability of failure}\\\\ \end{minipage}}$