$($AB Testing$)$ You are a Data Scientist tasked with conducting an experiment to measure the

effect of a webpage redesign on click rate for a link of interest. The current click rate is estimated

at hat$(p{)}_A=0\mathrm{.}015.$ The experiment you carry out is as follows: show the webpage to $n=500$ subjects

and record whether they click on the link of interest or not. You will use this experiment to

estimate the click rate $p_B$ for the new page design $($version B$).$ When you carry out your exper$-$

iment, you record that $20$ subjects clicked on the link of interest. Assuming a prior distribution

is beta with parameters $=2,=100$ :

a$.$ Compute and plot the posterior distribution for $p_B.$

b$.$ What is the probability that the new webpage has a higher click rate?