If n= 12 and `sumu_(i)v_(i)= 60`, where `u_(i)" and "v_(i)` are deviations of X and Y series from their respective means, then `cov(X, Y)` is

Options

A. `10`
B. `7.5`
C. `6`
D. `5`

Answer

To find the covariance of X and Y, we can use the formula for covariance, which is given by:

\[ \text{cov}(X, Y) = \frac{\sum (u_i \cdot v_i)}{n} \]

where:
- \( n \) is the number of pairs,
- \( u_i \) is the deviation of X from its mean,
- \( v_i \) is the deviation of Y from its mean.

Given:
- \( n = 12 \)
- \( \sum (u_i \cdot v_i) = 60 \)

Now, let's substitute the given values into the formula:

1. **Calculate the covariance**:
\[ \text{cov}(X, Y) = \frac{60}{12} \]

2. **Perform the division**:
\[ \text{cov}(X, Y) = 5 \]

Thus, the covariance of X and Y is \( 5 \).

### Summary of Steps:
1. Identify the formula for covariance.
2. Substitute the given values into the formula.
3. Perform the calculation to find the covariance.