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

Hint:

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Answer 1

The Correct Option is A, C

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 $