--- title: "HW 2" author: "Name here" date: "Due January 25, 2017 at 5:00 PM" output: html_document --- Please use D2L to turn in both the HTML output and your R Markdown file in. ### 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: - an attacking team rolls three dice and the defending team rolls two dice. - each team's highest two rolls are compared in a pair, for instance if the attacking team rolls (6-4-2) and defending team rolls (4-4), then the pairs would be (6-4) and (4-4). - within each pair, if there are any ties the defending team wins that outcome. Specifically if: - attacking team rolls (6-4-2) and defending team rolls (4-4), each team wins one point. - attacking team rolls (6-6-2) and defending team rolls (6-6), defending team wins two points. - attacking team rolls (5-4-2) and defending team rolls (4-2), attacking team wins two points **Estimate the probability that the attacking team wins two points**. This can be done analytically or through simulation. ```{r } attack <- sample(x = 1:6, size = 3, replace = T) defend <- sample(x = 1:6, size = 2, replace = T) ```