The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is

Options

A. 0.48
B. -0.48
C. 0.5
D. -0.5

Answer

To find the correlation coefficient \( r \) of a bivariate distribution given the regression coefficients \( b_{y|x} \) and \( b_{x|y} \), we can use the formula:

\[ r = \sqrt{b_{y|x} \cdot b_{x|y}} \]

### Step-by-Step Solution:

1. **Identify the Regression Coefficients**:
- Given \( b_{y|x} = -0.64 \) (the regression coefficient of Y on X)
- Given \( b_{x|y} = -0.36 \) (the regression coefficient of X on Y)

2. **Substitute the Values into the Formula**:
- Substitute the values into the formula for the correlation coefficient:
\[ r = \sqrt{(-0.64) \cdot (-0.36)} \]

3. **Calculate the Product**:
- Calculate the product of the regression coefficients:
\[ (-0.64) \cdot (-0.36) = 0.2304 \]

4. **Take the Square Root**:
- Now take the square root of the product:
\[ r = \sqrt{0.2304} \]

5. **Final Calculation**:
- Calculate the square root:
\[ r \approx 0.48 \]

Thus, the correlation coefficient \( r \) of the distribution is approximately **0.48**.