more work

R/ch2.qmd

@@ -543,4 +543,27 @@ are likelihoods. We are determining how likely each value of
 $\pi$ is given that we have observed $Y = 1$.
 :::
 
+We can formalize the likelihood function $L$ in our example
+as follows:
+
+$$L(\pi|y=1) = f(y=1|\pi) = {6 \choose 1}\pi^1(1-\pi)^{6-1}$$
+$$ = 6\pi(1 - \pi)^5$$
+
+We can test this out
+
+```{r}
+6 * .2 * (.8 ^ 5)
+```
+which is the value we get as .2 in the bar plot above.
+
+the likelihood values for $Y = 1$ are here:
+
+```{r}
+d |>
+    filter(ys == 1)|>
+    select(-display_pi) |>
+    knitr::kable()
+```
+
+