is the expected value of choosing a random positive integer infinity?

[torn lake]

🤔

[dreamy mountain]

The probability of choosing a random positive integer with a uniform probability on positive integers is 0, hence if you consider any random variable counting the times a certain integer is picked, the expected value will be 0

[wide elbow]

Sometimes, it makes sense in mathematics but feels so absurd in real life

[dreamy mountain]

I know right haha

Even more absurd, I claim that if X is a random variable counting the number of times you end up choosing an integer in an arbitrarily large (finite) set of integers, the answer is still 0 🥲

[wide elbow]

Now this just flabbergasted me

[torn lake]

I see

Because you multiply each by the percent chance they will get chosen

So even though there are infinite numbers and basically infinitely large numbers that can be chosen

Because it's an infinite set, each one has a infinitely low chance of being picked

That sucks

[dreamy mountain]

That's the idea, yeah 👍

[torn lake]

!solved

/solved

.closed

.close