I have this probability problem:
On any given day Eric is either cheerful (C), so-so (S), or glum (G).
If he is cheerful today, then he will be C, S, or G tomorrow with respective probabilities 0.5, 0.3, 0.2.
If he is feeling so-so today, then he will be C, S, or G tomorrow with probabilities 0.3, 0.4, 0.3.
If he is glum today, then he will be C, S, or G tomorrow with probabilities 0.2, 0.2, 0.6.
I have generated 50,000 independent pseudo-random numbers (uniform) in R and have printed out the first 40. Now, how do I use the 1st random number to chose the initial state X0 at random (1/3 probability for each state)? I know that this is equivalent to generating a discrete random variable, but I am still confused.
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