VisualizationsStatistics and Probability

Advanced Probability

Slide the chances of sunny turning rainy and rainy turning sunny, then step forward. The sunny-rainy split settles into a steady balance.

Markov Chain

Markov Chain Simulator

Observe convergence to the stationary state as the transition matrix powers update the state probability vector over time.

Transition Rates

P(State A → State B)0.30

P(State B → State A)0.40

TRANSITION MATRIX P

[

0.700.300.400.60

]

Rows sum to exactly 1.0

State Transition Diagram

Probability State Distribution

Sunny A:100.00%

Rainy B:0.00%

Transition Steps:0

Stationary Target:[57.1%, 42.9%]

Regardless of which state you start from (Sunny or Rainy), repeated multiplication by the transition matrix converges to the same stationary distribution.

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