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 Jul 6 comment Guessing the length of a playlist on “shuffle random?” The distribution of repeats shouldn't give additional information, because the selection of which song is repeated is a random process (whereas whether any other song is heard is not random, since it is dependent on the number of other songs left) Apr 13 comment Find the expected value of a dice sum What is the probability that it will take m rolls? What is the distribution of X over those m rolls? Apr 13 comment What philosophical consequence of Goedel's incompleteness theorems? I think the entire idea that you can write an essay in Philosophy of Science about Goedel's theorem and its implications is what Arturo/Andre are criticizing. Apr 11 comment Probability distribution of markov chain I mean that when we write down the stochastic matrices, we usually write them down as right stochastic matrices unless otherwise stated. Sorry for the confusion. Apr 11 comment Probability distribution of markov chain On the left - that's where the name comes from. A left stochastic matrix is defined as one where all the columns sum up to 1. This is essential because, when you end up doing the matrix multiplication, you'll see that each state has a total probability 1 of going to any other state - which only makes sense. Same thing for right stochastic matrices. Apr 11 comment Probability distribution of markov chain It should be $\pi M^2$. This is a "right stochastic matrix" (rows sum up to 1), which means it's on the "right" of a matrix multiplication. It is my understanding that transition matrices are by convention situated on the right. I'm not sure why this is so; maybe someone else can enlighten us.