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Question #59875

Difficulty: 8/10 | 🟢 Free

The Question

Let $X$ be a discrete random variable taking values in the set $S = \{3, 6, 9\}$ . A student incorrectly assumes that $X$ is uniformly distributed over $S$ . Later, the true probability mass function is found to be $P(X=x) = k(-5x^2 + 57x - 72)$ for $x \in S$ , where $k$ is a constant. Let $\sigma^2$ be the true variance of $X$ . The value of $100 \sigma^2$ is:

Options

A.
441
B.
369
C.
600
D.
450

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Monster

Ultra-high difficulty questions designed to test your limit, stamina, and deep conceptual understanding.

Concepts Behind This Question

Correction of Incorrect Mean/Variance|Probability Mass Function (PMF)|Equiprobable Outcomes

Why This Question Is Tricky

Examiner Levers

Concept Bridge

Cross-chapter synthesis (e.g., using Logarithms in Electrochemistry).

Difficulty Boost : +5

Common Mistakes

This question tests the correction of a probability distribution by properly normalizing a given weight function.

The primary trap lies in the 'Equiprobable Outcomes' assumption, which students might incorrectly blend with the new PMF.

The secondary trap is the numerical distractor '369', which emerges exactly as the unnormalized sum of squares if the student reduces the probability ratios to 3:5:2 but forgets to divide by the sum of these weights (10).

This creates a false sense of confidence, leading them to select 369 instead of completing the full variance calculation.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Statistics - Class 11
Concept	Correction of Incorrect Mean/Variance
Difficulty	8
Cognitive Load	7
Target Solve Time	170 sec
Access	Free