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Compute Markov steady state and expectations

DRWData Scientist · Onsite
MediumData ScientistOnsiteStatistics & Math

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Compute Markov steady state and expectations evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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).