4.73 What happens if the correlation is not zero? Suppose that X is a random variable with mean 30 and standard deviation 4. Also suppose that Y is a random variable with mean 50 and standard deviation 8. Assume that the correlation between X and Y is 0.5. Find the mean of the random variable Z for each of the following cases. Be sure to show your work.

1. (a) Z = 35 − 10X.

2. (b) Z = 12X − 5.

3. (c) Z = X + Y.

4. (d) Z = X − Y.

5. (e) Z = −2X + 2Y.