A Puzzling Expected Value

A puzzling expected value

Pick a (uniformly) random real number from the unit interval [0,1] and repeat this until the sum of all chosen numbers exceeds 1. What is the expected number of real values you will pick?

The quite surprising answer is Eulers constant, e ≈ 2.71828.

A demonstration can be found on Wolfram MathWorld.

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More Posts from Science-is-magical and Others

8 years ago

Does the name “Pavlov” ring any bells?


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3 years ago
A Falcon 9 Moon : Illuminating Planet Earth’s Night, Full Moons Can Have Many Names. This Year The

A Falcon 9 Moon : Illuminating planet Earth’s night, full moons can have many names. This year the last full moon of northern hemisphere summer was on September 2, known to some as the Full Corn Moon. A few days earlier on August 30 this almost full moon rose just before sunset though, shining through cloudy skies over Cape Canaveral Air Force Station on Florida’s Space Coast. A well-timed snapshot caught the glare of rocket engines firing below the lunar disk, a Falcon 9 rocket’s first stage successfully returning to Cape Canaveral’s landing zone 1. About 9 minutes earlier, the same SpaceX Falcon 9 rocket had launched the SAOCOM 1B satellite toward polar orbit. The fourth launch for this reusable Falcon 9 first stage, it was the first launch to a polar orbit from Cape Canaveral since 1969. via NASA


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8 years ago
One Of The Best Ways To Get People To Do Something Is To Make It Fun. A Marketing Campaign Called ‘The

One of the best ways to get people to do something is to make it fun. A marketing campaign called ‘The Fun Theory’ found that when stairs next to an escalator were turned into giant, functional piano keys, the amount of people who took the stairs increased 66%, and when a trash can had sound effects that made it seem infinitely deep, people started picking up and throwing away litter just to hear it. Source


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7 years ago
Chaotic Behaviour In 50-link Pendulum.

Chaotic behaviour in 50-link pendulum.


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7 years ago

Today is Copernicus’s 540th birthday. You may remember Copernicus as the man who said “Hey, what if the Earth went around the sun?” To which the Catholic Church replied “Hey, what if we set you on fire?” 


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8 years ago

I hate when people get all snobby like “uhm, humans didn’t EVOLVE from apes, humans and apes share a common ancestor”

Yeah well guess what shitlips, that common ancestor? an ape. By every taxonomical definition, it would be considered an ape.

.. I mean shit, by taxonomical definition, humans still are apes. They fall under the family Hominidae. We didn’t ditch that branch when we put pants on.


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3 years ago
Jupiter’s South Pole, Taken By Cassini

Jupiter’s south pole, taken by Cassini


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8 years ago

A reminder that NASA isn’t the only space agency

I have seen many “Space achievements 2015” articles and posts leaving international accomplisments completely out, so here are some of them: 

1. A new type of basaltic rock on the moon was found by Chinese robotic lander.

China National Space Administration’s Chang’e-3 landed on the Moon on 14 December 2013, becoming the first spacecraft to soft-land since the Soviet Union‘s Luna 24 in 1976.

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2. On February 11, the European Space Agency, ESA, successfully launched on a suborbital trajectory and recovered an experimental wingless glider, IXV.

It became the first true “lifting body” vehicle, which reached a near-orbital speed and then returned back to Earth without any help from wings.

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3. On December 9, Japan’s Akatsuki spacecraft succeeded entering orbit of Venus.

Japan Aerospace eXploration Agency’s Akatsuki is the first spacecraft to explore Venus since the ESA’s Venus Express reached the end of its mission in 2014.

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4.  ESA’s Rosetta spacecraft detected oxygen ‘leaking’ from comet 67P/Churyumov-Gerasimenko, the first time these molecules have been seen around a comet.

Rosetta spacecraft, the first to drop a lander (named Philae) on a comet, entered orbit around 67P in 2014 and continues to orbit the body. On June 13, European Space Operations Centre in Darmstadt, Germany, received signals from the Philae lander after months of silence.

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5.  The Canadian Space Agency has provided NASA with a laser mapping system that will scan an asteroid that could potentially hit the Earth in about 200 years

A Reminder That NASA Isn’t The Only Space Agency

6. The high-resolution stereo camera on ESA’s Mars Express captured this sweeping view from the planet’s south polar ice cap and across its cratered highlands and beyond.

A Reminder That NASA Isn’t The Only Space Agency

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8 years ago
Photographs Taken Of Saturn By NASA. Yes, These Are Real Pictures; They Are Not Illustrations. 
Photographs Taken Of Saturn By NASA. Yes, These Are Real Pictures; They Are Not Illustrations. 

Photographs taken of Saturn by NASA. Yes, these are real pictures; they are not illustrations. 

(Source)


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