The coefficient of correlation between X and Y is 0.6 U and V are two variables defined as `U=(x-3)/(2), V=(y-2)/(3)`, then the coefficient of correlation between U and V is

Options

A. 0.1
B. 0.3
C. 0.2
D. 1

Answer

To find the coefficient of correlation between the variables U and V, we will follow these steps:

### Step 1: Identify the given correlation coefficient
The coefficient of correlation between X and Y is given as:
\[ r_{XY} = 0.6 \]

### Step 2: Define the transformations for U and V
The variables U and V are defined as:
\[ U = \frac{X - 3}{2} \quad \text{and} \quad V = \frac{Y - 2}{3} \]

### Step 3: Determine the scaling factors
From the definitions of U and V, we can identify the scaling factors:
- The scaling factor for U with respect to X is \( b_{UX} = \frac{1}{2} \).
- The scaling factor for V with respect to Y is \( b_{VY} = \frac{1}{3} \).

### Step 4: Use the formula for the correlation coefficient
The relationship between the correlation coefficients can be expressed as:
\[ r_{UV} = b_{UX} \cdot b_{VY} \cdot r_{XY} \]
Substituting the values we have:
\[ r_{UV} = \left(\frac{1}{2}\right) \cdot \left(\frac{1}{3}\right) \cdot r_{XY} \]

### Step 5: Substitute the known values
Now substituting \( r_{XY} = 0.6 \):
\[ r_{UV} = \left(\frac{1}{2}\right) \cdot \left(\frac{1}{3}\right) \cdot 0.6 \]

### Step 6: Calculate the product
Calculating the product:
\[ r_{UV} = \frac{1}{6} \cdot 0.6 = \frac{0.6}{6} = 0.1 \]

### Conclusion
Thus, the coefficient of correlation between U and V is:
\[ \boxed{0.1} \]