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13 Jun 2020
A small town has two public library branches, ๐ด and ๐ต. Patrons checking out books can return them to any of the branches, where the books stay until checked out again. Suppose that of the books borrowed from ๐ด, 40% are returned to ๐ต. Of the books borrowed from ๐ต, 50% are returned to ๐ด. (A) Find the stochastic matrix for this situation. (solution) (B) If a book is borrowed from ๐จ, what is the probability that it ends up at ๐ฉ after 5 more circulations? Use the idea of eigenvalues and eigenvectors. If you just multiply a matrix 5 times using a calculator in order to get your answer, you will get no credit for this problem at all.
A small town has two public library branches, ๐ด and ๐ต. Patrons checking out books can return them to any of the branches, where the books stay until checked out again. Suppose that of the books borrowed from ๐ด, 40% are returned to ๐ต. Of the books borrowed from ๐ต, 50% are returned to ๐ด. (A) Find the stochastic matrix for this situation. (solution) (B) If a book is borrowed from ๐จ, what is the probability that it ends up at ๐ฉ after 5 more circulations? Use the idea of eigenvalues and eigenvectors. If you just multiply a matrix 5 times using a calculator in order to get your answer, you will get no credit for this problem at all.
Jyotsana PrakashLv10
11 Feb 2021