Is it wrong to multiply the average number of occurences for a single period by the desired number of periods, to get an overall average? I'm working on a stats problem and I want to know if this is bad practice. (If it's reasonable, it'll save me a ton of time coding a different solution.)
During a day, an average of 3 events occur. If I want to know the average number of events in some number of days (for a Poisson distribution) can I just multiply the average number of occurrences by the desired number of days to get an overall average? The events are independent.
So, for two days the average number of occurrences is 6, for three days it's 9 etc.
 A: Adding to the answer by @Milos, you’re assuming that the average number of events per day follows Poisson distribution. We know that for independent variables
$$
X_i \sim \mathsf{Poisson}\left(\lambda_i\right)
$$
the distribution of their sum is
$$
\sum_{i=1}^n X_i \sim \mathsf{Poisson}\left(\sum_{i=1}^n \lambda_i\right)
$$
So if you can assume that the variables are independent and identically distributed, you can just multiply daily average by the number of days.
A: You're interested in the mean, that is, the expected number of events over $n$ days.
You can model the number of events on day $i$ with a random variable $X_i$ ($i=1,2,\ldots, n$).
So, the number of events in the period of $n$ days is:
$$
\sum_{i=1}^{n} X_i
$$
The expected value of the sum is the sum of expected values:
$$
E\left[ \sum_{i=1}^{n} X_i \right] = \sum_{i=1}^{n} E[X_i]
$$
regardless of the distributions that those variables follow.
So, if all the days have the same expected value (say $\mu$), then, yes, the expected value over $n$ days will be $n\cdot \mu$.
