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.

  • $\begingroup$ Weird problem. The interpretation $Y=3X$ is physically highly implausible. More plausible is that $Y=X_1+X_2+X_3$, where the $X_i$ have the same distribution as the $X$ for Town A, and are independent. $\endgroup$ – André Nicolas Feb 20 '16 at 0:09
  • $\begingroup$ I agree with Andre, but the author (whoever wrote the problem) should know better; '3 times that of town A' literally means $3X$. If they wanted Andre's interpretation they really should have written 'the sum of 3 iid variables'. It is very well understood that in general $3X \neq X_1+X_2+X_3$. $\endgroup$ – Em. Feb 20 '16 at 1:29

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


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