Question:
Let 𝑋 be a continuous random variable having the 𝑈(−2, 3) distribution. Then which of the following statements is correct?
Let 𝑋 be a continuous random variable having the 𝑈(−2, 3) distribution. Then which of the following statements is correct?
Updated On: Jan 25, 2025
- \( 2X + 5 \) has the \( U(1, 10) \) distribution
- \( 7 - 6X \) has the \( U(-11, 19) \) distribution
- \( 3X^2 + 5 \) has the \( U(5, 32) \) distribution
- \( |X| \) has the \( U(0, 3) \) distribution
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The Correct Option is B
Solution and Explanation
1. Transformation for \( 7 - 6X \): - If \( X \sim U(-2, 3) \), then: \[ 7 - 6X \sim U(7 - 6 \cdot 3, 7 - 6 \cdot (-2)) = U(-11, 19). \]
2. Analyze Other Options:
(A): \( 2X + 5 \sim U(-4 + 5, 6 + 5) = U(1, 11) \), not \( U(1, 10) \).
(C): \( 3X^2 + 5 \) is not uniform because squaring \( X \) creates a non-linear transformation.
(D): \( |X| \) creates a piecewise distribution, not \( U(0, 3) \).\\
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