This is from a past stat exam that I am studying for my final tomorrow (lol). I believe this might have to do with gamma function. Could someone guide me through step by step of how to do this?
An insurance company knows that major flooding occurs in a town on average every three years and there is reason to believe that the probability is exponentially distributed.
What is the expected time for the next two floods to occur?
What is the probability that two major floods will occur within the next 6 to 12 years?
Also, relating confidence intervals, I'm confused as to when to use 2-sided versus a 1-sided in a problem
You need to look at the Gamma distribution and its expected value
The gamma distribution takes two parameters $\alpha$ and $\beta$
you can think of $\Gamma(\alpha,\beta)$ as the time required for $\alpha$ events to occur given that these events occur randomly in a Poisson process with the mean time between events as $\beta$
So (a) this is simply the expected value of $\Gamma(2,3)$, the time for 2 events to occur with a mean time of 3. Given the expected value of the gamma distribution (check wikipedia) this is simply is $3*2$ or 6 years for the next two floods to occur
Given this do you know what to do for (b)? HINT you need to use the CDF for the gamma distribution. The answer is $\approx 0.31$, can you see why?