Answer :
Answer:
the variance of X is 81.
Step-by-step explanation:
Given:
Covariance (cov(x, y)) = 27
Correlation coefficient (r) = 0.6
Variance of Y (σ²y) = 25
We can use the formula:
cov(x, y) = r * σx * σy
where σx is the standard deviation of X, and σy is the standard deviation of Y.
Rearranging the formula to solve for σx, we get:
σx = cov(x, y) / (r * σy)
Substituting the given values, we get:
σx = 27 / (0.6 * √25)
= 27 / (0.6 * 5)
= 27 / 3
= 9
Now, we can find the variance of X (σ²x) by squaring the standard deviation of X:
σ²x = σx²
= 9²
= 81
Therefore, the variance of X is 81.