Given mean and standard deviation of the number of accidents in Town A, find mean and variance in Town B.

Question

I'm having some trouble figuring out this question:

The number of car accidents in Town A has mean $2.3$ car accidents per hour with standard deviation of $1.5$ car accidents per hour. It is known that the number of car accidents in Town B is $3$ times that of Town A. Given this information, what is the mean and variance of the number of car accidents in Town B?

Been stuck on this for a while and I'm just not really sure how to begin to approach this problem.

Answer 1

Let $X$ be the number of accidents in town A, and $Y$ the number in town B. Then the relationship is $$Y = 3X.$$ Then, recall the properties:

1. $E[Y] = E[cX] = cE[X]$ and

2. $\text{Var}(cX) = c^2\text{Var}(X).$