# Concept derivation guides

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Concept guide



## [Discrete-time stochastic process: marginals and two-time joint laws from a complete path distribution, with Markov and stationarity checks](/en/derivations/derivation-mko-discrete-stochastic-process-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-discrete-stochastic-process)

Horizon {0,1,2}, states {0,1}. The complete path support with exact PMF is (0,0,0):1/4, (0,1,1):1/4, (1,0,1):1/8, (1,1,0):1/8, (1,1,1):1/4. (1) Check the support and the PMF, build the probability space and explain why X_0, X_1, X_2 are random variables on the same space; (2) find the marginal law at each time and the joint law of (X_1,X_2); (3) prove that this process is neither stationary nor Markov; (4) construct a path law with the same marginals but a different joint law, showing that the marginal tables are not the whole process.

Discrete-time stochastic process

derivation-mko-discrete-stochastic-process-01





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