Question Bank • QB_EM_162 MCQ • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Correlation and regression analysis

Question Statement:

The Pearson correlation coefficient $r$ between two random variables $X$ and $Y$ always lies strictly in the range:

Options:

  • (A) $-1 \le r \le 1$
  • (B) $0 \le r \le 1$
  • (C) $-\infty < r < \infty$
  • (D) $-0.5 \le r \le 0.5$

Answer Key:

A

Step-by-Step Solution & Explanation

By the Cauchy-Schwarz inequality, the correlation coefficient $r = \frac{\text{Cov}(X, Y)}{\sigma_X \sigma_Y}$ satisfies $-1 \le r \le 1$.
← Previous (QB_EM_115) Next (QB_EM_161) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test