ABRACADABRA! The magic of martingales скачать в хорошем качестве

ABRACADABRA! The magic of martingales

Welcome to the first video upload of this channel! I'm George Lowther and will post on a variety of mathematical topics, starting with martingales. Martingale theory is a branch of probability with many applications. Here we look at the time taken for random events to occur - a Monkey typing Shakespeare, or typing abracadabra, the time taken to toss two heads in a row with a fair coin, two sixes with a regular dice and so on. Simple gambling strategies can be used to cut out much of the complicated math and go direct to the answers we want. The profit and loss of such gambling games follow martingale processes. 00:00 The infinite monkey theorem/Intro 01:48 Time to type Shakespeare 03:44 Monkey typing ABRACADABRA! 06:28 Coin tossing 13:24 Ad hoc calculations 17:08 The martingale technique 20:46 Waiting for a sequence to appear 28:22 Monkey typing ABRACADABRA - the martingale proof 32:11 Generating functions using martingales 37:31 Outro The result about the monkey typing abracadabra has appeared in other videos here on YouTube, in particular there is a fantastic one by Mihai Nica:    • A Coin Flip Paradox and the ABRACADABRA Th...   I thank Mihai for his help and encouragement in learning the Manim software used for the mathematical animation. (You might notice the similarity between the coin flips in his video and in mine!) Music used in the intro, outro and title clips is "Almost Sure" by Alex Gonatas:    • Almost Sure  . I thank him for giving his kind permission to include here