Simpson's Paradox with Poisson Scoring

In a basketball game, teams A and B each play two halves. Let $X_{A,1}$ and $X_{B,1}$ be the points scored by A and B in the first half, and $X_{A,2}$ and $X_{B,2}$ in the second half. Assume each $X_{i,j} \sim \text{Poisson}(\lambda_{i,j})$ and all four are independent. 1. Construct specific parameters $\lambda_{A,1}, \lambda_{B,1}, \lambda_{A,2}, \lambda_{B,2}$ such that A is more likely to outscore B in each individual half, but B is more likely to win the overall game. (This is Simpson's paradox.) 2. Prove that your construction works by computing the relevant probabilities. You may use numerical approximations. 3. Interpret this phenomenon in the context of evaluating trading strategies on conditional vs. aggregate performance metrics.