On any given day a receptionist is either cheerful (c) or gloomy (g). Suppose th
ID: 3005677 • Letter: O
Question
On any given day a receptionist is either cheerful (c) or gloomy (g). Suppose that whether or not the receptionist will be cheerful tomorrow depends on her mood only through the last two days. Specically, suppose that if she was cheerful yesterday and today, then she will be cheerful tomorrow with probability 0.8; if she was cheerful yesterday but not today then she will be cheerful tomorrow with probability 0.3; if she is cheerful today but not yesterday then she will be cheerful tomorrow with probability 0.4; and if she was gloomy yesterday and today then she will be cheerful tomorrow with probability 0.2. (I) Compute the one-step transition probability matrix of the above Markov chain. (Hint: This is a four state M.C.) (ii) What proportion of days is the receptionist cheerful? gloomy?
Explanation / Answer
(1) MATRIX ch ch ch 0.8 ch gl ch 0.3 gl ch ch 0.4 gl gl ch 0.2 (2)2:3 &1:3 ANS
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