Hey guys, got few questions on likelihood and MLE stuff and hope to get some help and advises on them please.

Question
Pr(X=x|p) = ((1-p)^(x-1)) * p , for x=1,2,3,...
Suppose you observe n and record x1, x2, ... , xn.

a) Write down your likelihood and find the MLE of p

b) Using Bayesian approach, assign a beta prior to 'p' and obtain the posterior distribution for p.

c) Compare the posterior mean of p to the MLE. What can you say about sensitivity of posterior inference to prior assumptions?

These are the questions, your help is needed and will be much appreciated.

Regards,