CUET · MATHS · PYQ PAPER 2025
Match List-I with List-II.
If the random variable z has the following distribution:
| X | 0 | 1 | 2 | otherwise |
| P(x) | k | k | 2k | 0 |
| List-I | List-II |
| (A) k | (I) \(\frac{3}{4}\) |
| (B) \(P(x \geq 2)\) | (II) \(1 / 4\) |
| (C) \(P(x \leq 2)\) | (III) \(\frac{1}{2}\) |
| (D) \(P(0<x \leq 2)\) | (IV) 1 |
- A (A) - (I), (B) – (III), (C) - (II), (D) - (IV)
- B (A) - (II), (B) - (III), (C) - (I), (D) - (IV)
- C (A) - (I), (B) - (IV), (C) - (III), (D) – (II)
- D (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
Answer & Solution
Correct Answer
(D) (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
Step-by-step Solution
Detailed explanation
\(\Sigma P(x) = 1\) \(k + k + 2k = 1\) \(4k = 1 \implies k = 1/4\) (A) \(k = 1/4 \implies\) (II) (B) \(P(x \geq 2) = P(2) = 2k = 2(1/4) = 1/2 \implies\) (III) (C) \(P(x \leq 2) = P(0) + P(1) + P(2) = k + k + 2k = 4k = 4(1/4) = 1 \implies\) (IV) (D)…
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