AP EAMCET · Maths · Probability
A random variable X follows a binomial distribution in which the difference between its mean and variance is 1. If \(2 \mathrm{P}(\mathrm{x}=2)=3 \mathrm{P}(\mathrm{x}=1)\), then \(\mathrm{n}^2 \mathrm{P}(\mathrm{x}>1)=\)
- A \(13\)
- B \(11\)
- C \(15\)
- D \(12\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\( np - np(1-p) = 1 \Rightarrow np^2 = 1 \) \( 2\binom{n}{2}p^2(1-p)^{n-2} = 3\binom{n}{1}p(1-p)^{n-1} \) \( n(n-1)p^2(1-p)^{n-2} = 3np(1-p)^{n-1} \) \( (n-1)p = 3(1-p) \Rightarrow np - p = 3 - 3p \Rightarrow np + 2p = 3 \)…
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