Accidents occur in a factory at the rate of 3 per week. Assume that accidents happen randomly and independently of each other.
What is the mean time(in weeks) to the first accident?
For this question, the mean is $u=\frac{1}{λ}$.
Which equals $u=\frac{1}{3}=.33$.
What is the variance of the time(in weeks) to the first accident?
Now, apparently I got the answer wrong for this question. Here's what I did, and I would love some feedback on what I did wrong.
The variance $v$ for the Exponential Distribution is $v=\frac{1}{λ^2}$.
Which equals $\frac{1}{λ^2}=\frac{1}{(\frac{1}{3})^2}=\frac{1}{\frac{1}{9}}=9$
So I concluded that the variance is $9$. But apparently it is wrong according to the automatic online grading system.
$\frac{1}{\lambda}=\frac{1}{3}$ does not imply that $\lambda=\frac{1}{3}$. Instead $\lambda = 3$, and so
$$v=\frac{1}{\lambda^2}=\frac{1}{3^2}=\frac{1}{9}.$$