3. CONVENIENCE STORES You own two convenience stores in Chicago. One in Hyde Park, and one in Humboldt Park. The number of customers that enter the Hyde Park location during a 1 hour period is Poisson distributed with parameter 10. The number of customers that enter the Humboldt Park location during a 1 hour period is Poisson distributed with parameter 12. Given that the locations are in different neighborhoods, we assume that the number of customers that enter each location are completely independent. Problem 3.1. Let X be the number of customers that enter both locations in a 1 hour period. What is X 's distribution? (Hint: To help you simplify this distribution, it 1will be useful to remember the classical Binomial theorem: For any real numbers my 6 IR and ingeger n 2 1, we can expand (I + y)\" = 2:20 RC]; Iky\"_k.)