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andson of a man from Harvard go andson of a man from Dartmouth

andson of a man from Harvard go andson of a man from Dartmouth

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. In the Dark Ages, Harvard, Dartmouth, and Yale admitted only male students. Assume that, at that time, 80 percent of the sons of Harvard men went to Harvard and the rest went to Yale, 40 percent of the sons of Yale men went to Yale, and the rest split evenly between Harvard and Dartmouth; and of the sons of Dartmouth men, 70 percent went to Dartmouth, 20 percent to Harvard, and 10 percent to Yale. (a) Find the probability that a grandson of a man from Harvard goes to Harvard. (b) Find the probability that a grandson of a man from Dartmouth goes to Yale. (c) What is the steady state distribution for this Markov chain? (d) Find the entropy rate Hoo for this Markov chain (you might find the formula Ho=E, P(S.)H(S.) useful).
Transcribed Image Text:1. In the Dark Ages, Harvard, Dartmouth, and Yale admitted only male students. Assume that, at that time, 80 percent of the sons of Harvard men went to Harvard and the rest went to Yale, 40 percent of the sons of Yale men went to Yale, and the rest split evenly between Harvard and Dartmouth; and of the sons of Dartmouth men, 70 percent went to Dartmouth, 20 percent to Harvard, and 10 percent to Yale. (a) Find the probability that a grandson of a man from Harvard goes to Harvard. (b) Find the probability that a grandson of a man from Dartmouth goes to Yale. (c) What is the steady state distribution for this Markov chain? (d) Find the entropy rate Hoo for this Markov chain (you might find the formula Ho=E, P(S.)H(S.) useful).
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