# Tag Info

### analytical asymptotic approximation of the expected maximum, mean, and minimum distance of nearest neighbours in unit ball

It helps to look at this abstractly. Suppose we're in a metric space at a fixed point $x_0$ and for any possible radius $r\ge 0$ the chance that a single random point lies within distance $r$ of $x_0$ ...
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Alternative derivation of $EX = \int_0^\infty \left(1-F_X(x)\right)\mathrm d x$ (for a positive r.v. $X$): For any $x \ge 0$ one has that $x=\int_0^x 1 \mathrm dt = \int_0^\infty \mathbf I_{t\le x}\... • 103 0 votes ### Expectation of binomial random variable It seems that what must have been meant was $$X\mid N \sim \operatorname{Binomial}(N,p)$$ and$\mu=\operatorname E(N).$In that case you have$\operatorname E(X\mid N) = Np$and then $$\... • 10.6k 1 vote ### I would like some insight into what I have been working on here Summarizing comments into an answer: When a potential customer opens the door and allows the salesperson into the house, then the salesperson must take the time to make the sales pitch. If the pitch ... • 95.6k 3 votes ### Formula for expectation that works both for the continuous and discrete cases To address your question on whether the expression$$ \int_{\mathcal{X}} x \, P(\text{d}x)$$is generic enough for both the continuous and discrete cases for the expectation of a random variable$X$: ... • 64k 4 votes Accepted ### Jensen's inequality for one of several variables The answer is actually no. Here is a counter-example. Consider$f(x, y) = e^{x+y}$. Assume that$X=1$with probability$1/2$and$X=-1$with probability$1/2$. Let$Y=-X$. Then you have that$f(X, Y) =...
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Day5 (last) Let $A,B$ be respective the min and max fish in hand. Let $t_5$ be our threshold for rerolling the minimum fish on day5. Let $E_{5}[{A,B}]$ be the value of having the option to reroll when ...