Econometrics/Statistics, variance and means

Question

here's the problem I can't figure out on my own: The weight of a randomly selected student, (W), has a mean of $170$ and variance of $10$. Defining the new random variable ($Y$): the total weight of two students carrying a $5$ lb backpack each. What is the mean and variance of ($Y$)?

I don't know if defining the constant, $5$, is worthwhile, or even the steps to take to solve this. Any help's greatly appreciated, thanks!!

Answer 1

Let $W_1,W_2$ denote the random variables for weights for the randomly selected students. Let $Y=W_1 + W_2 + 10.$ Assuming $W_1$ are $W_2$ are independent, we get:

$E[Y]=E[W_1+W_2+10] = E[W_1]+E[W_2]+E[10] = 170 + 170 + 10 = \boxed{350}$

and

$Var[Y]=Var(W_1 + W_2+10) = Var(W_1) + Var(W_2) + Var(10)= 10+10+0=\boxed{20}$