Poisson question If you have crime statistics, say for 12 months, with a total of x. You divide that number to get, say 13 incidents per month.
Now, assuming that these data follow a Poisson distribution, what I'd like to be able to predict is the likelihood of being a crime victim. However, I'm not sure I am using this data correctly.
In R, I might do a Poisson function like this (where 1 is the number of occurrences, and 13 is mu): 
dpois(1,13) 
# 2.938428e-05

But, isn't that result really saying that the prob of only 1 crime event in a month is small, NOT that YOUR prob of being a crime victim is this number?
So, I'm not sure how to use the crime statistics to predict the likelihood of being a crime victim.
 A: First you need to know the size of the population (n) that you are considering: are you one person in one hundred, one thousand, one million? I guess you will assume that when a crime happens, every person is as likely to be the victim? Then you need to sum over all the possible outcomes of number of crimes times their probability and multiply by $\frac{1}{n}$:
$$P(X|\mu,n) = \frac{1}{n}  \sum_{i=0}^\infty i*f_{Poisson}(i|\mu) = \frac{\mu}{n}$$
with X the event of you falling victim to a crime and $f_{Poisson}$ the density function of the Poisson disribution. As you see from the last equality this is just the average number of criminal events per month $\mu$ divided by the size of your population n.
Keep in mind that the assumption of equal probability of being a victim is most probably wrong. You are merely calculating the average probability of a randomly drawn individual from your population
.
A: The question is not well defined - what is the time period you are interested in? Clearly being a victim at least once in 80 years has a much higher probability than being a victim at least once during one day. When you decide upon a length of time T (measured, say, in years), you calculate the probability 1-P(Y(T)=0) where Y(T) has a Poisson distribution with a parameter xT/n. x is the observed number of 
crimes in one year, n is the size of the population, T is the number of years you are asking about (can be a fraction of a year also, but has to be measured in years). You need to calculate 1-P(Y(T)=0) because in theory you can be hit more than once (if n is not very large).
Of course this assumes a uniform distribution of crimes over the population, which is probably not accurate.
