AP EAMCET · Maths · Probability
For a binomial variate \(X\) with \(n=6\), if \(P(X=2)=9 P(X=4)\), then its variance is
- A \(\frac{8}{9}\)
- B \(\frac{1}{4}\)
- C \(\frac{9}{8}\)
- D 4
Answer & Solution
Correct Answer
(C) \(\frac{9}{8}\)
Step-by-step Solution
Detailed explanation
Given that \(n=6\) and \(\begin{aligned} & P(X=2)=9 P(X=4) \\ \Rightarrow \quad{ }^6 C_2 p^2 q^4 & =9 \cdot{ }^6 C_4 p^4 q^2 \end{aligned}\) \(\begin{aligned} \Rightarrow \quad 9 p^2 & =q^2 \\ p & =\frac{1}{3} q \end{aligned}\) \(\because\) We know that \(p+q=1\)…
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