IF `cov(X, Y)= -8, Var(X)= 1.44" and "Var(Y)= 100`, then coefficient of correlation between X and Y is

Options

A. `(2)/(3)`
B. `(3)/(4)`
C. `-(3)/(4)`
D. `-(2)/(3)`

Answer

To find the coefficient of correlation between X and Y, we can use the formula:

\[ r = \frac{cov(X, Y)}{\sqrt{Var(X) \cdot Var(Y)}} \]

### Step-by-step Solution:

1. **Identify the given values:**
- Covariance \( cov(X, Y) = -8 \)
- Variance \( Var(X) = 1.44 \)
- Variance \( Var(Y) = 100 \)

2. **Substitute the values into the formula:**
\[ r = \frac{-8}{\sqrt{1.44 \cdot 100}} \]

3. **Calculate the product of the variances:**
\[ 1.44 \cdot 100 = 144 \]

4. **Calculate the square root of the product:**
\[ \sqrt{144} = 12 \]

5. **Substitute back into the formula:**
\[ r = \frac{-8}{12} \]

6. **Simplify the fraction:**
\[ r = -\frac{2}{3} \]

### Final Answer:
The coefficient of correlation \( r \) between X and Y is \( -\frac{2}{3} \).

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