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

Given information
- Covariance between the two variables = 20
- Variance of one of the variables = 16

Calculating the variance of the other variable
To find the variance of the other variable, we can use the formula for covariance:

Cov(X,Y) = E((X - E(X))(Y - E(Y)))

Where Cov(X,Y) represents the covariance between variables X and Y, E() represents the expected value or mean, and X and Y are the variables.

We can rearrange the formula to solve for E(XY):

Cov(X,Y) = E(XY) - E(X)E(Y)

Since we are given the covariance (Cov(X,Y) = 20), we can substitute it into the equation:

20 = E(XY) - E(X)E(Y)

Substituting the given variance
Next, we substitute the given variance of one of the variables (Var(X) = 16) into the equation. Variance is defined as the covariance of a variable with itself, so we can rewrite the equation as:

20 = Var(X) - E(X)E(Y)

Since Var(X) = E(X^2) - (E(X))^2, we can substitute it into the equation:

20 = E(X^2) - (E(X))^2 - E(X)E(Y)

Using the formula for variance
Finally, we can use the formula for variance to calculate the variance of the other variable. The variance of a variable Y is defined as:

Var(Y) = E(Y^2) - (E(Y))^2

We can rearrange the equation to solve for E(Y^2):

Var(Y) + (E(Y))^2 = E(Y^2)

Now, we can substitute the calculated value of E(Y^2) into the equation:

Var(Y) + (E(Y))^2 = 20 + E(X)E(Y) + (E(X))^2

Since we are given the variance of one of the variables (Var(X) = 16), we can substitute it into the equation:

Var(Y) + (E(Y))^2 = 20 + 16 + E(X)E(Y) + (E(X))^2

Simplifying the equation, we get:

Var(Y) + (E(Y))^2 = 36 + E(X)E(Y) + (E(X))^2

Conclusion
In conclusion, the variance of the other variable (Var(Y)) would be equal to 36 + E(X)E(Y) + (E(X))^2. To calculate the exact value of the variance, we would need the expected values of the variables X and Y.