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2 votes

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 $x_0$ ...
whuber's user avatar
  • 328k
0 votes

Find expected value using CDF

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}\...
Flo's user avatar
  • 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 $$ \...
Michael Hardy's user avatar
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 ...
EdM's user avatar
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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 $X$: ...
Robert Long's user avatar
4 votes

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) =...
ECL's user avatar
  • 155
0 votes

expected value of a fishing strategy

The approach works the same as the dice problem, but now you work with the lightest fish instead of a single fish. You try to improve the expected value of the lightest fish and by doing that you ...
Sextus Empiricus's user avatar
0 votes

expected value of a fishing strategy

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 ...
enryuxbt's user avatar

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