Please use D2L to turn in both the HTML output and your R Markdown file in.

### Q1. (6 pts)

Assume you are trying to model the probability that an MSU student is wearing a Patagonia jacket or sweater. Consider three different prior distributions:

- Beta(.01, .01)
- Beta(100, 1)
- Normal(\(\mu = .5\),\(\sigma^2 = .1^{2}\))

Plot the figures, on the same scale, and discuss the differences in the prior distributions.

### Q2. (6 pts)

Assume you surveyed a random selection of MSU students and identified that 78 of the 100 students in your survey were wearing Patagonia. Use JAGS to fit the posterior distribution for each prior distribution. Report the posterior HDI for each prior. Make sure to include (print) R code in the document.

### Q3. (6 pts)

Select and justify a prior (this could be one of the three above, but need not be.). With this prior calculate and summarize your posterior. Describe the results in the context of MSU students and Patagonia clothing.