Binomial distribution: f(x/n) = (x) p*(1-p)*-* n = number of customers enter the shop at one day x = number of customers that wearing a mask when entering the shop Assume p = 0.8 and x = 8 1. Find the MLE of n and plot the likelihood vs n graph. 2. From the previous observations, the number of customers enter the shop at one day expects to be around 12. Evaluate a prior distribution for n (both the parameters and the type) and explain it. 3. Find the posterior distribution for n (as the product of the likelihood and prior). 4. Find the posterior mean.