Solve Markov and distribution expectation problems
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This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Solve Markov and distribution expectation problems states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.
Question
Given a finite Markov chain, how do you find its stationary (steady-state) distribution? State and derive the expected value of an exponential distribution and of a Poisson distribution. For a non-singular square matrix A, express the sum of the eigenvalues of A⁻¹ in terms of the eigenvalues of A and explain why. In a specified two-player game-theory scenario, calculate the probability of a particular outcome.
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