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Q1. (4 pts)

Describe the differences between probability density functions and probability mass functions.

Q2. (8 pts)

Assume you have been given a special set of dice and tasked with learning the probabilities of each side being rolled. Desribe the 5 steps of a Bayesian data analysis in the context of this problem.

Q3 (8 pts)

After a recent Strangers Things binge, you have taken up board games. Your roommate Billy Hargrove challenges you to a game of Risk. To understand the strategy you need to think about the following scenario:

Specifically if:

Estimate the probability that the attacking team wins two points. This can be done analytically or through simulation.

attack <- sample(x = 1:6, size = 3, replace = T)
defend <- sample(x = 1:6, size = 2, replace = T)