Question 1: Amazon is a well-known global online shopping website. Assume you are hired as the data scientist to understand the potential customers' arrival behavior. After analyzing historical data, you find the number of customers entering the website can be modeled as a Poisson distribution with mean parameter 20 persons per hour.

i) How long will it take, on average, to see a potential customer enters the website and starts browsing? (Ans: 3 minutes)

ii) Assume the browsing time of a potential customer can be described by an exponential random variable with mean 2 minutes. John is a potential customer and has visited the website for 2 minutes. What is the probability that he will leave the website in next 2 minutes? (Ans: 0.632) (Hint: Google "memoryless exponential distribution")

Question 2: The lifetime of a certain manufacturer's washing machine is normally distributed with mean 3 years. Only 15% of all these washing machines last at least 5 years. What is the standard deviation of the lifetime of a washing machine made by this manufacturer? (Ans: 1.93)