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Markov chains find direct applications in genetics. Here is an example: An offspring of a black...

Markov chains find direct applications in genetics. Here is an example:

An offspring of a black dog is black with probability 0.6 and brown with probability 0.4.

An offspring of a brown dog is black with probability 0.2 and brown with probability 0.8.

(a) Write the transition probability matrix of this Markov chain.

(b) Rex is a brown dog. Compute the probability that his grandchild is black.

Math   Statistics-And-Probability   
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