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How to calculate expected values using the Darth Vader Rule? Also: How did I make this video?!?! A live-ish coding tutorial of how I programmed all the animations in this video in the Python package Manim. In particular using MathTex objects to animate equations. [Some bug hunting edited out of the "live" stream!] *Link To Final Python Notebook Used To Make the Video* https://github.com/mcnica89/manim/blo... *Other Helpful Docs* Manim Docs: https://docs.manim.community/en/stabl... Manim in Google Colab instructions: https://docs.manim.community/en/stabl... Google Clab itself: https://colab.research.google.com/ *My Full Production Process* 1. Use Manim to create the animations! (This video!) 2. Render them in high quality using -qh tag in manim and save them as ordinary videos. 3. Use OBS studio screen recorder (free!) to record myself with a ChromaKey filter for greenscreen with videos in background. I use a wireless keyboard to press "spacebar" to pause/play the video at the appropriate times, and include a longer DELAY in the animations to make room for this in the video. 4. Edit the video in Davinci Resolve (free version!) and remove pauses where I am waiting around for the animation to happen. 5. Use Adobe audio enhance (free version!) to enhance the audio. (In this video only the first 8:35 are enhanced...there is a 30 minute maximum). Make sure to set the audio to stereo when you use it!!! *Chapters* 00:00 Darth Vader Rule for Expected Values 01:00 Proof of the Darth Vader Rule 03:52 Find the Expected Number of Coin Flips Until First Heads 06:10 Summing the Geometric Series 8:35 Manim Tutorial in Jupyter Notebook 12:13 Manim Draw a Circle 14:25 Global variable for DELAY 15:15 Making the main video 16:07 MathTex object and using r 18:25 Moving things around in Manim 21:10 Align by splitting MathTex object as a list of parts 26:20 Buffer command buff= 28:29 SurroundingBox command 31:10 Default Manim Colors 32:37 Using VGroup to group things together 36:37 eqn_1_alt with coefficients 39:01 Hack to make part of the MathTex bigger 40:38 Animate things using Transform command to morph things 43:55 Making a copy with .copy() 48:25 Animate a list of animations 55:01 Animate in boxes 56:11 LaggedStart to stagger the FadeOuts 1:00:05 move_to command to stack mobjects 1:02:35 ReplacementTransform is needed! 1:08:35 Copying Mobjects to start a new scene 1:16:35 Align things using a loop 1:25:35 Animate the Coinflip example 1:41:30 Edge of sanity Music: Ambient Wave 48 (Tribute) by Erokia -- https://freesound.org/s/496757/ -- License: Creative Commons 0 Sneaky Adventure Kevin MacLeod Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/b...