and use that as an estimate of the population variance. And, as you probably know if you are reading this, since there is additional uncertainty as to the population variance, when we use these results to estimate the mean we will need to widen the credible interval by using Student's t table instead of the standard normal table.

So, to continue with the previous example, where Arnie had a normal (30,4

^{2}) prior. Suppose we have only 5 observations: 31.1,28.2,34.2,35,31.5.

We calculate the sample variance:

In R:

In Python:

The weights are:

The posterior mean is then:

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