**11-1.** Conduct a prior predictive simulation for the reedfrog model. By this I mean to simulate the prior distribution of the tank survival probabilities $\alpha_j$. Start by using this prior: \begin{align} \ _{j} Normal(\overline{}, ) \\ \ \overline{} Normal(0, 1) \\ \ Exponential(1) \\ \end{align} Be sure to transform the $\alpha_j$ values to the probability scales for plotting and summary. How does increasing the width of the prior on $\sigma$ change the prior distribution of $\alpha_j$? You might try Exponential(10) and Exponential(0.1) for example. ```{r 11-1} ``` **11-2.** Revisit the reed frog survival data, data(reedfrogs). Start with the varying effects model from the book and lecture. Then modify it to estimate the causal effects of the treatment variables `pred` and `size`, including how size might modify the effect of predation. As easy approach is to estimate an effect for each combination of `pred` and `size`. Justify your model with a DAG of this experiment