Two newspapers compete for subscriptions in a region with

Chapter 1, Problem 57E

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Two newspapers compete for subscriptions in a region with 300,000 households. Assume that no household subscribes to both newspaper and that the following table gives the probabilities that a household will change its subscription status during the year. From AFrom BFrom NoneTo ATo BTo None.70.20.10.15.80.05.30.20.50For example, an interpretation of the first column of the table is that during a given year, newspaper A can expect to keep 70% of its current subscribers while losing 20% to newspaper B and 10% to no subscription.At the beginning of a particular year, suppose that 150,000 households subscribe to newspaper A, 100,000 subscribe to newspaper B, and 50,000 have no subscription. Let P and x be defined by .The vector x is called the state vector for the beginning of the year. Calculate Px and P2x and interpret the resulting vectors