Question

For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =

Options

• 4/5

• 1/5

• 1/3

• 2/3

   

• None of these

Answer 1

n =3

\[P(X = 1) = 8 P(X = 3) (\text{ Given } )\]
\[\text{ The distribution is given by } \]
\[P(X = r) =^{3}{}{C}_r \left( p \right)^r \left( q \right)^{3 - r} \]
\[P(X = 1) =^{3}{}{C}_1 \left( p \right)^1 \left( q \right)^2 \text{ and } P(X = 3) =^{3}{}{C}_3 \left( p \right)^3 \left( q \right)^0 \]
\[ \Rightarrow 3p q^2 = 8 p^3 \]
\[ \Rightarrow 8 p^2 = 3 q^2 \]
\[ \Rightarrow 8 p^2 = 3(1 - p )^2 \]
\[ \Rightarrow 8 p^2 = 3 - 6p + 3 p^2 \]
\[ \Rightarrow 5 p^2 + 6p - 3 = 0\]
\[ \Rightarrow p = \frac{- 6 \pm \sqrt{96}}{10}\]

Hence , it does not match any of the answer choices.