In office hours, I tend to get three types of questions. Easy questions (e.g., What went wrong in my solution here?) require a minute to respond to. Medium questions (e.g., What good are random variables in the real world?) require 4 minutes. Hard questions (e.g., How do I become a better student?) take 10 minutes. Based on experience, about 60% of questions are easy, 30% are medium, and 10% are hard.

(a) Define a random variable for this setting in words and in symbols, state its support, and give its probability model.

(b) What is the average time I spend responding to a student question, and what is the standard deviation in my response times? (Include units on answers, as always.)