Michael
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 Jul2 awarded Curious Jan24 comment What is the expectation of the product of two random variables of Dirichlet distribution? I apologise for my incorrect edit. I thought you use $\alpha_i = \alpha - \alpha_j$ and $\alpha \Gamma(\alpha) = \Gamma(\alpha+1)$ to get the second step of $E(X_i \log X_i)$ Jan24 revised What is the expectation of the product of two random variables of Dirichlet distribution? I added more explanations to explain the steps Jan24 suggested approved edit on What is the expectation of the product of two random variables of Dirichlet distribution? Jan24 comment What is the expectation of the product of two random variables of Dirichlet distribution? Whoa! Thank you so much! You are a genius. Do you have any recommendations for a good book on Dirichlet distribution? I could not find any references that talk about joint Dirichlet distribution. Jan24 accepted What is the expectation of the product of two random variables of Dirichlet distribution? Jan24 comment What is the expectation of the product of two random variables of Dirichlet distribution? can you show me how? Thanks! Jan24 revised What is the expectation of the product of two random variables of Dirichlet distribution? added 9 characters in body Jan24 revised What is the expectation of the product of two random variables of Dirichlet distribution? edited title Jan24 comment What is the expectation of the product of two random variables of Dirichlet distribution? Thank you very much for your answer. Do you have the form for $E[X_i \ln(X_j)]$? Jan24 revised What is the expectation of the product of two random variables of Dirichlet distribution? added 584 characters in body Jan24 comment What is the expectation of the product of two random variables of Dirichlet distribution? @Lost1 I apologise for the poor English, I have amended the question. My main question is how to derive $E[X_i \ln(X_j)]$ Jan24 revised What is the expectation of the product of two random variables of Dirichlet distribution? added 2 characters in body; edited title Jan23 asked What is the expectation of the product of two random variables of Dirichlet distribution? Sep23 comment How to prove that the product of a decreasing monotonic function and a strictly increasing monotonic function is a concave function? @Oleg567 It is possible. Consider segment [0,1], and functions $f(x) = x, g(x) = e^{-x/5}$ Sep20 asked How to prove that the product of a decreasing monotonic function and a strictly increasing monotonic function is a concave function? Sep18 comment Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points @JonasMeyer I mean to say that the optimal point is a local maximum. My mistake in confusing turning point to be local maximum Sep18 comment Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points Thank you for your clarifications, I am sorry for mistaken turning point to be local maximum, which I was asking. Sep18 revised Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points deleted 47 characters in body Sep18 comment Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points Great answer! Is there a set of conditions that need to be fulfilled in order to ensure $h$ has a point of inflection?