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JEE Mains · Maths · STD 12 - 13. probability
A random variable \(X\) has the following probability distribution
| \(X\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
| \(P(X)\) | \(K^2\) | \(2K\) | \(K\) | \(2K\) | \(5K^2\) |
- A \(\frac{7}{12}\)
- B \(\frac{23}{36}\)
- C \(\frac{1}{36}\)
- D \(\frac{1}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{23}{36}\)
Step-by-step Solution
Detailed explanation
\(\sum P(X)=1 \Rightarrow K^{2}+2 K+K+2 K+5 K^{2}=1\) \(\Rightarrow 6 \mathrm{K}^{2}+5 \mathrm{K}-1=0 \Rightarrow(6 \mathrm{K}-1)(\mathrm{K}+1)=0\) \(\Rightarrow \mathrm{K}=-1\) (rejected) \(\Rightarrow \mathrm{K}=\frac{1}{6}\)…
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