Suppose that there are 3 possible states of the weather in the fall: "sunny", "cloudy" and "rainy". Suppose that if the weather is sunny on one day, then on the following day it will be sunny with probability 0.4, cloudy with probability 0.3 and rainy with probability 0.3. Moreover, if the weather is cloudy on a given day, then it will never be sunny on the following day, but it might be cloudy again with a probability of 0.8 or rainy with a probability of 0.2. Finally, if the weather is rainy on any given day, it will be sunny on the following day with a probability of 0.2, cloudy with a probability of 0.3 and rainy with a probability of 0.5. a) Write the transition matrix A corresponding to the Markov chain described above. b) On any given day, what is the transition matrix B describing the probabilities of being in the states "sunny", "cloudy" and "rainy" two days from now?

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.