Let Z1, Z2, ... be a sequence of independent and identically distributed random variables having discrete uniform distribution over {1, 2, ..., 2024}. Let Yn = ∑i=1n Zi for n ≥ 2. Further, let Xn be the remainder when Yn is divided by 2025. Then, which of the following statements is true?

Five people stand at the vertices of a regular pentagon, throwing frisbees to each other. They have two frisbees, initially at adjacent vertices. In each time step, each frisbee is thrown independently to the left or right vertex with equal probability (1/2). The process ends as soon as one person is the target of two frisbees simultaneously. What are the mean and variance of the number of pairs of throws?