Question 37

Mathematics Statistics Medium

Suppose values taken by a random variable \(X\) are such that \(a \leq x_{i} \leq b\), where \(x_{i}\) denotes the value of \(X\) in the \(i^{\text {th }}\) case for \(i=1,2,3, \ldots n\), then

(A) \((b-a)^{2} \geq \operatorname{Var}(X)\)
(B) \(\frac{a^{2}}{4} \leq \operatorname{Var}(X)\)
(C) \(a^{2} \leq \operatorname{Var}(X) \leq b^{2}\)
(D) \(a \leq \operatorname{Var}(X) \leq b\)
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Correct Option is D. Practice regular variations of this Statistics concept to build speed and accuracy.

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