Finding the mean of a random variable in an equation given standard deviation and mean

Question

Please help! What do I plug into these equations to solve for the mean of Z??

Suppose that X is a random variable with mean 23 and standard deviation 5. Also suppose that Y is a random variable with mean 40 and standard deviation 9. Find the mean of the random variable for each of the following cases:

Z= 2 + 10X, Z= 2X - 10, Z= X + Y, Z= X - Y, and Z= -5X - 2Y

Answer 1

Hints:

• $\mathbb E(U+V)=\mathbb E(U)+\mathbb E(V)$.

• $\mathbb E(cU)=c\mathbb E(U)$ where $c$ denotes a constant.