Making Probability Mathematical | Infinite Series

"saying something has probability 0, does not mean it's impossible"... yes it does; that is exactly what it means.

Bayes theorem

A paradox arises from requesting an infinitely small area from a granular universe.

I had no idea that probability has had so many rigors apply to it so relatively recently.

Phil Dunphy is not a square!

This video should be shown at the first class of every probability course ...

Why exactly must the chance you hit (x, y) with a dart be zero? If you were to integrate all the probabilities over the entire dartboard you'd get a total chance of hitting the board equal to 0, which is weird.

well, the probability that she reads this comment on such an old video is zero

Hmm 🤔 Of the tens of thousands of gods created by man... On which one of those shall I place my wager? Please advise!

Wow, now I can understand more Monte Carlo.

Im in love... (withh all respect) of you as well of the content in this channel and every pbs channel! Cheers from Mexico!

Let's talk about focal points!
Sorry.

Wow. Intelligence is so sexy.

so "Pascal's Wager" is basically the "it'd cost you exactly $0.00 to be kind" meme

If there are an infinite amount of exact points on the board, why doesn't that mean the probability of hitting one is infinitesimally small but not 0? Cause with the other examples like 1/4 the area fits on the board 4 times, with 1/2 it fits twice, so I was like if it fits on the board infinite amount of times it'd be 1/infinity? I'm just a layman so forgive me if I'm being stupid

Bayes Theorem is my favourite.

be there or be square came about because if you're not there you're not "a round". also it rhymes

I suppose probabilities is basic to quantum computations.

Beautiful women. Thank you for being explaining maths!

I (we) miss you

Unfortunately very very basic. It's good for kindergarden pupils, though. Thanks for wasting my time!

Craps is my favorite thing about probability!😎

Well it's not rational to believe in God, since in most major religions, the greater sin than to not believe in God, is to believe in a false God, and since we can't know which God is the real God, its more rational to not believe at all in a God.

My favorite part of probability?


AdDiNG FrACtiOnS

I was looking for something with more history to be fair. Especially the axiomatic approach of Kolmogorov's vs the limit approach for probability, and early origins of what happened afterwards.

I'm interested in the use of elementary probability to aid in rational decision making.

Easy PROVE GOD EXISTS
A GREAT SPIRITUAL TEACHER WILLCOME.
He will CARRY
1) Buddha on his back. Buddha thought that you were to avoid those who impeded your progress. When he became to fat to walk. They left him for he impeded their progress.
2) Allah is a clot in his ankle, Muhammad was a leetch and his teachings were not written down till years later so they are not his.
3) Shiva' rides on his calf. The worship the cow but it's his calf the deity rides that is holy, not the cow.
4) Confucius hangs from his chin
5) Christianity is a boil on his ass
6) he will have SAP on his back from the cross he was crucified upon
7) he will have God's wrath upon his knee, but his wrath has heart.
8) he will have kinky on his two feet for he is Kin too the Key; or holy and worthy of religious veneration.
9) The baha faith is a noose around his neck. The snake charmer.
10) he will have a gold fouled anchor with 7 links symbolic of uniting the world as one nation under Seven Seas. Extending the rights of Americans to the World.
A nation born in a day.
11) he will have True North Compass about him. A moral compass for the World to follow. It was written he would have great compassion but it's a poor translation. He will have Compass about him.

ALL are leeches on the body of christ. If you follow one religious path you all follow them all for Jesus Carrie's them all upon his body as proof to his identity. A gift from god.

I give you my body. It is covered in what look like scars but they're spiritual markings plain as day just like a tattoo.

God says to warm you before you get ate. Consumed as devil's food for having hate in your heart. 7 8 9
And OU812.

Murderous math. Killing the Son of God and steeling his book and recovering it making him an icon of the very religion he refused to convert to.
Taken by murder. A crimson stain of a blue blood.

Greating people of earth, I'm BACK

rubbish explanation

Bro why omit the origin of probability?
The earliest known forms of probability and statistics were developed by Arab mathematicians studying cryptography between the 8th and 13th centuries.
Most miracles originated in Levant.

I feel bad for the person who posed so happily to be called as "a boring and old fashioned person" XD

Kolmogorov is easily one of the top 3 mathematicians of all time.

My favourite aspect of probability is knowing how often I'll hit a straight or flush draw when the other players at the table have no clue

How do you get randomness from the definition used for random variable?

What is your opinion of a man that has a Mathematical equation or formula to predict winning Mega Millions numbers and Powerball numbers?

These axioms are hard ru define, I've tried.

why haven’t you guys posted :(

Google

She's pretty

I may write something very boring but I don't see any connection between this work and science (mathematics especially). Seeing this I wonder what makes people doing such videos - if not money then what? Let's suppose that the text was written by a person who knows the field deeply (otherwise it's an absurd) then I can't understand how could the text be written so uninformative. Basically, the only mathematical thing mentioned was the intuitive understanding of measure as an area. There are three categories of people. People learning maths understand that the theme is much harder then it was shown so they won't benefit from it - waste of time. People who want to learn maths would likely feel an impression that it's easy so that when they will learn it would tough or even disappointing trying to prove basics (for example, showing that vitali set is not measurable). And eventually the third category of people who are far from maths will just rubbish their mind (human's mind is obviously limited, unfortunately). Tell me, please, how these videos get so much positive feedback.
I have already learned measure theory on the level to prove properties related to lebesgue integral - read book by J oxtoby (and other book by scientists from MSU). Finally, made categotical definition of a mesurable function as a morphism between measurable spaces (don't blame me for using category theory, I can understand people, who don't take it seriously)

Pascal's Wager assumes he believes in the correct God. But there are so many!

apparently probability is just the study of proportions

“ NERRDS!”

Its not Probably......Its Problem Ability.....

It Is Problem Ability= ProbAbility

Gerolamo Cardano who lived in the first half of the 16th century and known as the first to publish methods that solved reduced cubics also expressed probability by ratio

I see this in 2024. But I have a question here. I'm not from a mathematical background. I feel measure theory as an axiomatic ground for probability is a problem. I think pascal and ferman did a great job by using calculas as a basis. What's funny is that even game theory is developed with this method but it's not practical usable in many places because of measure theories axiomatic conditions. I think the foundation of modern probability has to change.

Tonight on a very special pbs infinite, a troubled gambler reaches out to a mathematician for help.

After learning about a lot of this and then going back to this video, it's quite nice how many things are brought up here