Fix expectation of s² and m in gdemo (#1927)

* Fix expectation of s² and m in gdemo

The expectation of m cannot be anything different from 0, given the definition. Likewise for an inverse gamma random variable. Former sentence, "the expectation of s is 49/24 (2.04166666...) and the expectation of m is 7/6 (1.16666666...)." cannot be correct.

* Update docs/src/using-turing/guide.md

Co-authored-by: Ramon Diaz-Uriarte <[email protected]>

* Update docs/src/using-turing/guide.md

Co-authored-by: David Widmann <[email protected]>

Co-authored-by: Hong Ge <[email protected]>
Co-authored-by: David Widmann <[email protected]>

Author: 3 people

docs/src/using-turing/guide.md

@@ -42,7 +42,12 @@ end
 ```
 
 
-Note: As a sanity check, the expectation of `s` is 49/24 (2.04166666...) and the expectation of `m` is 7/6 (1.16666666...).
+Note: As a sanity check, the prior expectation of `s²` is `mean(InverseGamma(2, 3)) = 3/(2 - 1) = 3` and the prior expectation of `m` is 0. This can be easily checked using `Prior`:
+
+```julia
+p1 = sample(gdemo(missing, missing), Prior(), 100000)
+```
+
 
 
 We can perform inference by using the `sample` function, the first argument of which is our probabilistic program and the second of which is a sampler. More information on each sampler is located in the [API]({{site.baseurl}}/docs/library).