Mary receives 22 messages in 5 hours according to a Poisson Process. What is the mean number of messages Mary receives in an hour?

Seems like a simple question, so just to confirm: Mean = 22/5

Isn't it?

  • $\begingroup$ It might be helpful to contemplate under what circumstances your answer might change if "according to a Poisson process" were changed or even omitted altogether. To what extent does, or should, your assumptions about a phenomenon determine your description of what actually happened? $\endgroup$ – whuber Sep 17 '18 at 19:56
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    $\begingroup$ @whuber I believe that even if Poisson Process is removed from this question - the answer stays the same. $\endgroup$ – user218970 Sep 18 '18 at 0:26

The units on the rate, say $\lambda$, should be messages per hour. First, do you have the right units? Trivially, $$\frac{22 \text{ messages}}{5 \text{ hours}}=\frac{22}{5} \text{ messages/hour}$$

Next, your $\lambda$ should be the average number of messages per hour. With a little thought on how an average is calculated, you should be feeling pretty decent.


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