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 Apr21 awarded Yearling Feb23 revised Independent exponential random joint distribution added mathjax to make question more clear Feb23 comment Independent exponential random joint distribution Please add some attempt to solve the problem and your own thoughts rather than just a homework question. Feb23 suggested approved edit on Independent exponential random joint distribution Feb21 accepted scores of individuals and evaluation Jan3 comment Proof that this set is convex set You need to define your set properly for anyone to understand the question. Jan3 revised Proof that this set is convex set mathjax improvement Jan3 suggested approved edit on Proof that this set is convex set Jan3 comment Eigenvectors of normal matrix Thanks @pre-kidney Jan3 comment Eigenvectors of normal matrix Please add some context or some attempt to solve this. Dec28 comment Why can triple integrals be used to represent the volume under a surface f(x,y) by setting f(x,y,z) = 1? normally when taking the triple integral in rectangular coordinates, we have $$\int\int\int f(x,y,z)\text{d}x\text{d}y\text{d}z = \int\int\int f(x,y,z)\text{d}V\,,$$ where $\text{d}V$ is an infinitesimal volume. And thus, to compute the entire volume under the surface, we set $f(x,y,z)=1$. Dec24 comment A probability function is determined on a dense set- Where is density used in the following proof? The fact that there is guaranteed to be an $x' \in D$ such that $x' > x$ is a use of the density of $D$ in $\mathbb{R}$. Dec24 comment A probability function is determined on a dense set- Where is density used in the following proof? When it says "Given $\epsilon > 0$, there exists $x' \in D, x'>x$ such that $$F(x) + \epsilon \geq F_D(x')$$" Dec24 revised scores of individuals and evaluation edited body Dec24 comment scores of individuals and evaluation You're right, that's not what I looking for, let me edit that Dec24 comment scores of individuals and evaluation Yes and $\max\{p_m \in \mathcal{T}\} = 9$ as well. But is this always true? - what if we take a larger terrain, say $\mathcal{T}'$ with $m \in \{1,2,...,2000\}$ with each agent $i$, $H_i = \{h_{i1}, h_{i2}, ..., h_{ik}\}$ for some $k \in \mathbb{N}$. Dec23 comment scores of individuals and evaluation Using your example, this was not the case, though. @MickA The maximum of $\mathcal{T}_1$ was $9$, but $S_1 = 7$ and $S_2 = 8$. I'm pretty sure my definition of $S_i$ reflects this example, but please inform me if it does not. You said that $S_i$ would be different for each agent $i$, but now you say it wouldn't be different (the maximum of the point values on the terrain). Dec23 comment scores of individuals and evaluation Done @MickA. What you have given as an example above for $S_i$ is correct and also I added $X_i^m$, although this is clear, right? $X_i^m$ is just the maximum value that can be attained with each starting point $m$ and heuristic set for an agent $i$, $H_i$. Dec23 revised scores of individuals and evaluation added 38 characters in body Dec22 comment scores of individuals and evaluation I have updated the question, by the way.