Introduction:
To determine the variance of the other variable, we need to know the covariance between the two variables and the variance of one of the variables. Covariance measures the linear relationship between two variables, while variance measures the dispersion or spread of a single variable.

Given:
Covariance (X, Y) = 20
Variance (X) = 16

Relationship between Covariance and Variance:
The covariance between two variables, X and Y, can be calculated using the formula:

Cov(X, Y) = E[(X - μx)(Y - μy)]

Where Cov(X, Y) is the covariance, E is the expected value, X and Y are the variables, and μx and μy are the means of X and Y, respectively.

The variance of a variable, X, can be calculated using the formula:

Var(X) = E[(X - μx)²]

Where Var(X) is the variance, E is the expected value, X is the variable, and μx is the mean of X.

Calculating Variance of the Other Variable:
To find the variance of the other variable, let's denote it as Y. We can start by rearranging the covariance formula:

Cov(X, Y) = E[(X - μx)(Y - μy)]

Expanding the equation:

Cov(X, Y) = E[XY - Xμy - Yμx + μxμy]

Since E[XY] = μxμy as per the covariance formula, we can simplify the equation:

Cov(X, Y) = μxμy - μxμy - μxμy + μxμy

Cov(X, Y) = 0

Conclusion:
From the equation above, we can see that the covariance between X and Y is zero. This implies that there is no linear relationship between the two variables. Therefore, the variance of the other variable, Y, is independent of the variance of X. Given that the variance of X is 16, we cannot determine the variance of Y based on this information alone. Additional information or assumptions about the relationship between X and Y would be required to calculate the variance of Y.