The daily summer air quality index (AQI) in St. Louis is a random variable whose PDF is f(x) = kx² (180 − x), 0 ≤ x ≤ 180 1. Find the value of k that makes this a valid PDF 2. A day is an "orange alert" if the AQI is between 100 and 150. What is the probability that a summer day is an orange alert day? 3. Find the expected value of the summer AQI