If `U=3X+1,V=Y+2` and `r_(XY)=0.6` then `r_(UV)` is

Options

A. `0.2`
B. `-0.2`
C. `0.6`
D. none of these

Answer

To solve the problem, we need to find the correlation coefficient \( r_{UV} \) given the transformations \( U = 3X + 1 \) and \( V = Y + 2 \), along with the correlation coefficient \( r_{XY} = 0.6 \).

### Step-by-Step Solution:

1. **Identify the transformations**: We have \( U = 3X + 1 \) and \( V = Y + 2 \).
- Here, \( a = 3 \) (the coefficient of \( X \)) and \( c = 1 \) (the coefficient of \( Y \)).

**Hint**: Look for the coefficients of the variables in the transformations to identify \( a \) and \( c \).

2. **Check the positivity of coefficients**: Both \( a \) and \( c \) are positive.
- \( a = 3 > 0 \)
- \( c = 1 > 0 \)

**Hint**: Ensure that both coefficients are greater than zero to apply the correlation property.

3. **Apply the correlation property**: There is a property of correlation coefficients that states:
\[ r_{aX + b, cY + d} = r_{XY} \]
if \( a > 0 \) and \( c > 0 \). In our case, since both \( a \) and \( c \) are positive, we can use this property.

**Hint**: Remember that the correlation coefficient remains unchanged under linear transformations when the coefficients are positive.

4. **Calculate \( r_{UV} \)**: Since the property holds, we have:
\[ r_{UV} = r_{XY} \]
Given \( r_{XY} = 0.6 \), we find:
\[ r_{UV} = 0.6 \]

**Hint**: Substitute the known correlation coefficient directly into the equation.

5. **Conclusion**: The value of \( r_{UV} \) is \( 0.6 \).

### Final Answer:
\[ r_{UV} = 0.6 \]