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JEE Main 2024 Mathematics question

MathematicsStatisticsJEE Main 2024

Let the mean and the standard deviation of the probability distribution

| X | α | 1 | 0 | −3 | |---|---|---|---|---| | P(X) | 1/3 | K | 1/6 | 1/4 |

be μ and σ, respectively. If σ − μ = 2, then σ + μ is equal to .

Answer: 5

Solution

K = 1 − 1/3 − 1/6 − 1/4 = 1/4. μ = α/3 + 1/4 − 3/4 = α/3 − 1/2 and E(X²) = α²/3 + 1/4 + 9/4 = α²/3 + 5/2. From σ = μ + 2: α²/3 + 5/2

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Question ID VK-011658