N people order a single donut from a shop at an average rate rate of 400 people per week. We also know that N is poisson distributed. Each person who orders a single donut, independent of each other, with probability 0.20.2, orders a vanilla dip donut with rainbow sprinkles. Obviously the best donut invented.
Let XX be the number of people that order vanilla dip donuts with rainbow sprinkles in a week.
Derive the PMF of XX.