List questions from expected-value

Published on 09 Apr 2026 - 13:55

199

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Cut a unit stick at $n-1$ random points. Expectation of product of fragment lengths is $\prod\limits_{k=n}^{2n-1}\frac1k$. Why?

Published on 13 Apr 2026 - 21:56

24

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Derive a formula approximating the mean of logit-normal distribution

Published on 08 Apr 2026 - 22:44

78

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Flipping an unfair coin, but the probability varies

Published on 13 Apr 2026 - 19:22

68

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Coupon Collector "Paradox"

Published on 13 Apr 2026 - 20:30

43

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Finding the mathematical expectation

Published on 10 Apr 2026 - 3:28

51

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Odd Streak of Heads

Published on 14 Apr 2026 - 22:28

545

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Conjecture: If $A,B,C$ are random points on a sphere, then $E\left(\frac{\text{Area}_{\triangle ABC}}{\text{Area}_{\bigcirc ABC}}\right)=\frac14$.

Published on 28 Mar 2026 - 14:05

71

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Invalid Conditional Probability - Expectation of Die Rolls

Published on 11 Apr 2026 - 23:46

41

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Jaynes 3.4 : Expectations

Published on 14 Apr 2026 - 15:36

67

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Using quantile function of eventually monotonic pdf to get something like an expectation

Published on 25 Mar 2026 - 6:19

71

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expectation of the product of Gaussian kernels and their input

Published on 13 Apr 2026 - 20:58

363

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Show that $\int_0^1\int_{1-y}^1\sqrt{(x-1)(y-1)(x+y-1)}\mathrm dx\mathrm dy=\frac{2\pi}{105}$.

Published on 16 Apr 2026 - 21:13

68

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Proving $\mathrm E[XY] = E[X] E[Y]$ whenever $X$ and $Y$ are independent random variables.

Published on 14 Apr 2026 - 19:49

706

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What is the expected area of a triangle in which each side is a random real number between $0$ and $1$?

Published on 15 Apr 2026 - 15:32

List Question

Infinite game of an unfair coin toss

Cut a unit stick at $n-1$ random points. Expectation of product of fragment lengths is $\prod\limits_{k=n}^{2n-1}\frac1k$. Why?

Derive a formula approximating the mean of logit-normal distribution

Flipping an unfair coin, but the probability varies

Coupon Collector "Paradox"

Finding the mathematical expectation

Odd Streak of Heads

Conjecture: If $A,B,C$ are random points on a sphere, then $E\left(\frac{\text{Area}_{\triangle ABC}}{\text{Area}_{\bigcirc ABC}}\right)=\frac14$.

Invalid Conditional Probability - Expectation of Die Rolls

Jaynes 3.4 : Expectations

Using quantile function of eventually monotonic pdf to get something like an expectation

expectation of the product of Gaussian kernels and their input

Show that $\int_0^1\int_{1-y}^1\sqrt{(x-1)(y-1)(x+y-1)}\mathrm dx\mathrm dy=\frac{2\pi}{105}$.

Proving $\mathrm E[XY] = E[X] E[Y]$ whenever $X$ and $Y$ are independent random variables.

What is the expected area of a triangle in which each side is a random real number between $0$ and $1$?

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