Question

Let a random variable X has mean $\mu_x$ and non-zero variance $\sigma ^2 _x$, and another X random variable Y has mean $\mu_y$ and non zero variance $\sigma ^2 _y$. If the correlation Y coefficient between X and Y is $\rho$, then which of the following is/are CORRECT?

• A. $|\rho| \leq 1$
• B. The regression line of Y on X is $y = \mu_y + \frac{\rho \sigma_x}{ \sigma_y} (x − \mu_x )$
• C. The variance of X − Y is $\sigma^2 _x + \sigma^2 _y − 2\rho \sigma_x \sigma_y$
• D. $\rho = 0$ implies X and Y are independent random variables

Answer 1

Answer: (A), (C)

$|\rho| \leq 1$

Answer 2

The correct Options are A and C : $|\rho| \leq 1$ AND The variance of X − Y is $\sigma^2 _x + \sigma^2 _y − 2\rho \sigma_x \sigma_y$