A wandering ghost travels between four regions of the island where it lives: Toronbo Shores, Koholint Prairie, Tabahl Wasteland, and Goponga Swamp. It moves each day according to a Markov chain as given in the diagram. (From a given region, each possible move is shown and is equally likely.) Goponga Swamp Koholint Prairie Tabah! Wasteland Toronbo Shores What fraction of days does the ghost spend in each region, after much wandering? Region Toronbo Shores Koholint Prairie Tabahl Wasteland Goponga Swamp Fraction of days spent there

A state vector X for a four-state Markov chain is such that the system is four times as likely to be in state 1 as in 3, is not in state 2, and is in state 4 with probability 0.2. Find the state vector X.

TOPIC: MARKOV CHAINS A housewife always uses one of three brands of detergent: "A", "B" or "C". Which one she buys depends inwhich of the three manufacturers is running a promotional campaign (with gifts such as combs, ornaments, etc.),etc.). Companies undertake such campaigns at random, regardless of whether or not competitors are running other campaigns at the same time.not running other campaigns at the same time. Brand "A" company runs a campaign ½ of the time, brand "B" runs a campaign 1/3 of the time, and brand "B" runs a campaign 1/3 of the time, and brand "C" runs a campaign 1/3 of the time.1/3 of the time, and "C" promotes 1/3 of the time. If the lady buys brand "A" on a certain occasion, the next time she will also buy brand "A".If she buys brand "A" on a certain occasion, the next time she will also buy brand "A", if your company is promoting or if neither of the other two is doing so.or she buys brand "B" if it is on promotion, but brand "A" is not, or she buys brand "C" if…

TOPIC: MARKOV CHAINSA market research firm conducted a household survey regarding preferences for three brands of detergents.three brands of detergents. The survey was conducted by interviewing the same housewives at the beginning of two consecutive months.consecutive months. The results of the survey are as follows: Beginning of month 1: 200 respondents showed a preference for the "Ace" brand, 120 for the "Bold" brand, and 180 for the "Clean" brand.for the "Clean" brand. C) If the pattern of profit and loss does not change in the following months, how many housewives are estimated to prefer each brand at the end of month 2?