**Exercise 3.11 (Regular bike ridership) **A university wants to know what proportion of students are regular bike riders, π, so that they can install an appropriate number of bike racks. Since the university is in sunny Southern California, staff think that π has a mean of 1 in 4 students, and a mode of 5/22. 1. Specify and plot a Beta model that reflects the staff’s prior ideas about π. 2. Among 50 surveyed students, 15 are regular bike riders. What is the posterior model for π? 3. What is the mean, mode, and standard deviation of the posterior model? 4. Does the posterior model more closely reflect the prior information or the data? Explain your reasoning. **Exercise 3.18 (More Beta-Binomial)** 1. Patrick has a Beta(3,3) prior for π, the probability that someone in their town attended a protest in June 2020. In their survey of 40 residents, 30 attended a protest. Summarize Patrick’s analysis using `summarize_beta_binomial()` and `plot_beta_binomial()`. 2. Harold has the same prior as Patrick, but lives in a different town. In their survey, 15 out of 20 people attended a protest. Summarize Harold’s analysis using `summarize_beta_binomial()` and `plot_beta_binomial()`. 3. How do Patrick and Harold’s posterior models compare? Briefly explain what causes these similarities and differences.

Exercise 2.8 (Flight delays) For a certain airline, 30% of the flights depart in the morning, 30% depart in the afternoon, and 40% depart in the evening. Frustratingly, 15% of all flights are delayed. Of the delayed flights, 40% are morning flights, 50% are afternoon flights, and 10% are evening flights. Alicia and Mine are taking separate flights to attend a conference. Mine is on a morning flight. What’s the probability that her flight will be delayed? Alicia’s flight is not delayed. What’s the probability that she’s on a morning flight? Exercise 2.14 (Late bus) Li Qiang takes the 8:30am bus to work every morning. If the bus is late, Li Qiang will be late to work. To learn about the probability that her bus will be late ( π ), Li Qiang first surveys 20 other commuters: 3 think π is 0.15, 3 think π is 0.25, 8 think π is 0.5, 3 think π is 0.75, and 3 think π is 0.85. Convert the information from the 20 surveyed commuters into a prior model for π . Li Qiang wants to update that prior model with the data she collected: in 13 days, the 8:30am bus was late 3 times. Find the posterior model for π . Compare and comment on the prior and posterior models. What did Li Qiang learn about the bus?

Logistic Regression