Mean of a Poisson Distribution Using R's rpois function

Question

I entered the following command in R:

my_pois <- replicate(100,rpois(5,10))

I believe this creates 100 sets of 5 numbers in which each set should have a mean of 10. However when I look at the mean of each column(set created), this is what I get:

[1] 10.8  9.4  9.0 11.2 11.6 11.6  7.8 12.4  9.6 11.0  9.6  9.8 10.0  8.6  9.8  8.6  9.4

 [18] 11.4 12.0  8.4 10.2 10.2 10.8 10.2  7.6  9.8  8.4 10.6 11.6  8.6  9.6 11.0 11.0 10.0

 [35]  9.8  9.2  8.2  8.2 10.2  9.0 10.4  9.2 10.4 10.0 11.8 13.8 10.2  9.8 12.4 10.4  9.8

 [52]  9.8  8.6  7.4  9.2  9.0  7.4  9.2  9.4 11.8  9.2  9.8 11.6  9.8 10.8  8.6 12.4 10.4

 [69]  9.4  9.4  9.0 11.2 10.6  9.4  9.6  8.2  9.6 10.6 10.6  8.2  9.2 10.0 11.2  9.0  9.6

 [86] 10.4  8.0 10.2  9.8  7.4  9.6  9.0  7.2  8.4 11.8 10.8  9.4 12.4 11.2 12.0

Shouldn't they all be 10 since we specified a mean of 10?

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Answer 1

You can calculate the mean of all the samples using the following.

  k <- apply(my_pois,2, function(x) mean(x))

You are creating a random sample which should be approximately equal to 10. Since your sample is small it is unlikely to equal 10 exactly. As your sample size grows the mean comes closer to 10.

Here is one source I would review

Mean of a Poisson Distribution Using R's rpois function

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