The profit for a new product is given by Z = 2X - 2Y - 7. We know that X and Y are independent random variables with Var(X) = 2 and Var(Y) = 2.7. What is the variance of Z?

To find the variance of a linear combination of independent random variables, we can use the following formula:

Var(aX + bY) = a^2 * Var(X) + b^2 * Var(Y),

where a and b are constants, and X and Y are independent random variables.

In this case, we have:

Z = 2X - 2Y - 7.

Let's calculate the variance of Z using the formula mentioned above.

a = 2, b = -2, Var(X) = 2, and Var(Y) = 2.7.

Var(Z) = (2^2) * Var(X) + (-2^2) * Var(Y)
= 4 * 2 + 4 * 2.7
= 8 + 10.8
= 18.8.

Therefore, the variance of Z is 18.8.