Convolutions | Why X+Y in probability is a beautiful mess

this was so helpful, thank you soooo much

Can anyone explain how we get the probability for each dice? Because it supposed to be 1/6 for each dice face and even if I use two dices, the probability shown in video at 5 th minute, I couldn’t understand 😢

Just Mind Blowing

Is there an equivalent to this but for subtracting random variables?

How are you doing it?
How did you do it??!?

algorithm comment

channel for those who ask "why"

When I first learned about convolution I was told to "slide one graph along the other" but this trick never made much intuitive sense. Thank you so much for explaining convolution intuitively.

I do like this guy but why not see him proving these theorems with these illustrations. Yes this is aimed at a general public but it would be amazing seeing proofs at this level of illustration.

can i get the demo?

Super cool! I never thought like that! You explained to us the simply deep reason why the convolution is used!

Awesome. Also want to notice.
Here you take a slice of the joint distribution (3d drawing) along the line x+y=s and get the probability of random variables X+Y.
If you take a slice along the line x*y=s (hyperbola), you get probability X*Y , isn't it beautiful!

I knew the integral formula. Now it's crystal clear

You are simply the best ❤

if i can like this video a million times, i would! You just saved a 25% assignment with the super clear explanation and amazing intuition and graphics.

I wish this video was available 15 years ago. Great as always

Why does they don't teach in this way I would have not failed and dropped out

I see there are some artifacts in the very initial continuous case visualization (viewing on 1080p monitor). It would be cool if those artifacts somehow shifted with each example you name. This is talking almost artistically rather than from a math perspective

what is the difference between convolution and correlation, please do answer

It looked very complex, and you made it easy to understand, thank you

My man, 3 blue 1 brown loves Fourier transforms so much, that his animation of the eye, his channel logo, is literally converting a function from time domain to frequency domain. What an amazing hidden gem, such a cool way to put Fourier transform animation into you logo. Amazing.

This reminds me of studying for actuary exam p

im on the verge of tears thank you

Thanks!

3Blue1Brown is the goat

Why do we integrate the product of two functions by dx, instead of ds! For me it feels like if we integrate by dx we get the sum only for this particular s value and then we should integrate second time by ds exhausting all the combinations. No? Where am I wrong?

i love this video

Heh, the fact that optical astronomy drops this one line "convolution" for calibration in photometry and it took me back to this video. "A ha!" moment if you will.

that was so interesting.

That’s pretty cool

I understand where the square root of 2 come from. The question is why it is not reflected in the theorem saying PDF of X+Y is convolution of f_x and f_y

where is the subsequent video that connects it to the Central limit theorem?

Ich habe es endlich verstanden. Danke euch!

Holy crap has anybody ever thought about this for trading

Grant - could you imagine doing a playlist about proofs, Automated theorem proving and mathematical thinking?

최고의 영상입니다. uniform distribution이 중첩되면서 점점 종 모양이 되어갈 때 마치 영화 올드보이 마지막 장면에서 사진첩을 한장씩 앞으로 넘기면서 미도가 자신의 딸임을 깨닫는 오대수의 감정을 느꼈네요. "설마 저게 정규분포가 된다고?"

you did not have to drag out a video teaching convolutions to be nearly 30 mins.
Do better next time.

It amazes me how much fanciness goes into those videos and you always manage to show just one example. I dont think humans just like llms can learn enough from just one example. If you really wanted to teach convolutions you'd show many examples. You'd draw the whole map so I can build the container for the concept you are trying to teach. The whole video i cannot conceptualize a convolution in my mind if you show me just one example no matter how pretty the pictures are. I love how you pay exorbitant attention to something extremely obvious and 2 minutes later end up explaing something as esoteric as the square root of 2 scaling factor. Every fckin time, Grant.

I like to watch these videos while doing chores in the background. As in, the chores are in the background. This is my main focus. Until I realise that it’s been over 4 hours and I still haven’t finished folding one basket of laundry. Like right now.

Did you know that the shape of a typical soccer ball ⚽️ is the combination of a dodecahedron and an icosahedron? It’s also a truncated gyroelongated pentagonal bipyramid.

Trunk-ate-ed jie-row-e-long-gate-ed pen-tag-on-al by-pi-ra-mid.

May I tell you something? Do you remember saying that math has a component of story, by which you referred to the mysteries, challenges and curiosity which draw people in the same way a piece of fiction draws its fan base in? Well, your approach in telling that story reminds me of Rebecca Sugar. First starting things off with something tender and calm, before dropping something that drives people’s curiosity up, and then telling a story or two that sound familiar but enter a few elements that’ll be relevant later, and then before we know it, it turns out everything you just told us was a part of a story we didn’t even notice

Thank you for providing such a visualized explanation. It's priceless.

Loved it

I need a worked out example for convolution of two continuous random variables. I’m confused with setting the bonds of integration

It is beautiful., Which software do you use , would you tell me please ?

So your pet assistant is clip-pi