# Tagged Questions

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### Boundary points of probability simplex

I have a very simple question for which I know the answer but I can not prove it! What are the boundary points of a probability simplex? I know every probability vector with one zero component lies ...
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### Convexity of Binomial Term

I am reading a book on the probabilistic method, and the following claim was made: $\dbinom{y}{n}$ is convex. Why is this the case?
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### Converting a Probability constraint to a Norm constraint

Let $\mathbf{z}$ be a $N\times 1$ complex vector. Let $\mathbf{u}$ be a $N\times 1$ random Gaussian vector whose entries are i.i.d with zero mean and $\sigma^2$ variance. Consider the following ...
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### Expected values of some properties of the convex hull of a random set of points

$N$ points are selected in a uniformly distributed random way in a disk of the unit radius. Let $P(N)$ and $A(N)$ denote the expected perimeter and the expected area of their convex hull. For what ...
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