CUET · MATHS · PYQ PAPER 2023
Probability distribution of random variable \(X\) is:
| x | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
| \(P(X)\) | \[3k\] | \(3k\) | \(2k\) | \(2k^2\) | \(3k^2\) | \(4k^2\) |
- A \(k=-1, \frac{1}{9}\)
- B \(k=-1\)
- C \(k=\frac{1}{9}\)
- D \(k=0,-9\)
Answer & Solution
Correct Answer
(C) \(k=\frac{1}{9}\)
Step-by-step Solution
Detailed explanation
\(\sum P(X) = 1\) \(3k + 3k + 2k + 2k^2 + 3k^2 + 4k^2 = 1\) \(9k^2 + 8k - 1 = 0\) \((9k - 1)(k + 1) = 0\) \(k = \frac{1}{9}\) or \(k = -1\) For \(P(X) \ge 0\): If \(k = -1\), \(P(X=0) = 3(-1) = -3\), which is invalid. If \(k = \frac{1}{9}\), all \(P(X)\) values are non-negative.…
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