Answer the following probability/statistics sub-questions: 1) Given a finite-state, irreducible, aperiodic Markov chain with transition matrix P (provided), compute its stationary distribution π by solving πP = π with ∑i πi = 1, and state why the solution is unique. 2) Let X ~ Exponential(λ) and N ~ Poisson(λ), with λ > 0. Derive E[X] and E[N] from first principles (integration/summation), showing intermediate steps. 3) For a 2×2 zero-sum game with payoff matrix to Player A given in the prompt, find the mixed-strategy Nash equilibrium and report the probability each player assigns to their first action (use probability calculations to justify the equilibrium).