CUET · MATHS · PYQ PAPER 2025
A random variable \(X\) has the following probability distribution:
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(X) | 0 | k | 2k | 2k | 3k | \(k^2\) | \(2 k^2\) | \(7 k^2+k\) |
- A \(\frac{3}{100}\)
- B \(\frac{1}{2}\)
- C \(\frac{5}{100}\)
- D \(\frac{7}{100}\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{100}\)
Step-by-step Solution
Detailed explanation
\( \sum P(X=x) = 1 \) \( 0 + k + 2k + 2k + 3k + k^2 + 2k^2 + (7k^2 + k) = 1 \) \( 10k^2 + 9k - 1 = 0 \) \( (10k-1)(k+1) = 0 \) \( k = \frac{1}{10} \) (since \(k\) must be non-negative) \( P(4 \( P(4…
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