1. Consider you play a game where you are given arandomly selected raffle numbered (1.1, 3.2, 3.4, 4.7), where each number appears once. Once you are given the first raffle, you are given the second raffle based on the first raffle number. Second raffle is randomly chosen from those that are larger than the first raffle number. If the first raffle number is 4.7, then we choose the second from all remaining three (1.1, 3.2, 3.4). Let X and Y be the first and second raffle numbers, respectively. Find Var(Y|X = 4.7).
2. The time for an emergency medical squad to arrive at a residential building in NYC is distributed as a normal distribution with mean 8 minutes and standard deviation 2 minutes. What is the probability that exactly two arrive within 10 minutes among 5 independent squats trips? (i.e., two arrive within 10 minutes and the remaining take more than 10 minutes).