(a) Some beta distributions. If $a<1$, we get a spike'' on the left, and if $b<1$, we get a spike'' on the right. if $a=b=1$, the distribution is uniform. If $a>1$ and $b>1$, the distribution is unimodal. Generated by beta_dist_plot.ipynb . (b) Some gamma distributions. If $a\leq 1$, the mode is at 0, otherwise the mode is away from 0. As we increase the rate $b$, we reduce the horizontal scale, thus squeezing everything leftwards and upwards. Generated by gamma_dist_plot.ipynb .