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Question #41092

Difficulty: 8/10 | 🟢 Free

The Question

Let $X$ be a continuous random variable uniformly distributed on the interval $[-2, 4]$ . Let $Y = |X^2 - 2X|$ and $f_Y(y)$ be the probability density function of $Y$ . Find the value of $21 f_Y\left(\frac{24}{25}\right) + 9 f_Y\left(\frac{5}{4}\right)$ .

Options

A.
21
B.
24
C.
18
D.
27

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Random Variable Mapping|Equiprobable Outcomes|Modulus Sign Dependency

Why This Question Is Tricky

Common Mistakes

This question tests the 'Modulus Sign Dependency' trap in random variable transformations.

Students often incorrectly assume a uniform transformation rule across the entire support of Y.

Because the mapping involves the absolute value of a parabola, the probability space folds non-uniformly.

For y in (0, 1), the local minimum creates 4 distinct pre-images, whereas for y > 1, there are only 2.

Failing to partition the support and count the roots correctly leads to missing density contributions.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Probability - Class 11
Concept	Random Variable Mapping
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free