Probability and Its Limits - Professor Raymond Flood

The modern theory of probability is considered to have begun in 1654 with an exchange of letters between Blaise Pascal and Pierre de Fermat, and has developed since then into the discipline which examines uncertain processes. For example, although on tossing a coin you have no idea whether you will obtain heads or tails we know that if you keep doing it then in the long run it is very likely that the proportion of heads will be close to a half. The lecture will discuss this and other examples of random processes e.g. random walks and Brownian motion.

[vectorshift]

One of the best lecturers on the planet.

[MrMonkeyspanner]

+GreshamCollege Thank you for the lecture.
You said you couldn't think of an easy way to prove the birthday paradox with the lecture hall.
May I suggest you hand round a year's calendar and ask everyone to put a dot on their birthday while you carry on with the lecture. Assuming everyone takes 10s to do so it would take just over half an hour. If you wanted it to start when you started talking about the birthday problem and finish when you were ready to move on (around 6 mins), you could print the calendar on 5 transparencies and pass them along the rows with attached marker pens asking people to put a dot in a random position in the square indicating their birthday. Would be interesting to then calculate how likely it was to have the distribution of birthdays found on that particular occasion in the hall.

[MoerreNoseshine]

The part with the IMHO most important implications starts at @25.11- the random walk. Especially the example with the school children. I wish more people would understand such aspects rather than all those boring games examples. Yes, that's how the math for it began, but it's also, I think, why only lovers of math care and the rest tune out - "why would I care?".

[LearnMoreDoBetter]

Alternative (in the gambling game, 23 min) finding probabilities of winning the game and the probablity of the complement event (probability of not winning the game ). Instead of counting YYYY and YYYM cases as equally likely outcomes, and because in reality for some outcomes there is no need to take the third or the forth trials (already it would be known that one of the players already won). Therefore we can calculate the probability of just winning by the following events: MM ( 0.5^2), MYM (0.5^3), YMM (0.5^3), , MYYM, YYMM, YMYM (each outcome with 0.5^4), then by adding them together ( P(Win) = 0.6875), while probability of losing will be 0.3125.

[zaidsserubogo]

What is interesting is that; if probability outcome is "limitted" to a given results say 1 regardless of evolutionary processes or mechanism, then the future of such results can no longer be judged randomly, but judged with predictable degree of certainty. And probability disappear with limitations.

[RonJohn]

Does the Birthday Problem presume a fair distribution of birthdays across the year? (Because, in the US at least, there are significantly more-than-expeceted births in July thru October, and less than expected during the other months.)

[qcislander]

Ummm... so the birthday game for "n" people (assuming that n <365) is to find

n!/365n, subtract the result from one (that gets the proportion), then multiply by n to get the most likely number?

[fritsvanzanten]

20:30 I was merely listening (instead of watching) and understood that at stake were 64 pints. ;-)

[hyperduality]

Randomness is dual to order
Certainty is dual to uncertainty -- The Heisenberg certainty/uncertainty principle
Subjective is dual to objective
Thesis is dual to anti-thesis, the Hegelian dialectic
Energy is dual to mass -- Einstein
Dark energy is dual to dark matter
Energy is duality, duality is energy!

[lqacwaz]

philosophical brain-workout : try to figure out what limsup _ { m -> +inf} liminf _ { n -> +inf } limsup _ { r -> +inf } f(p, q, r) means intutively where f(p, q, r) is a function from {the set of nonnegative integers}^3 to nonnegative integers.

[glutinousmaximus]

Birthday problem - he forgot leap years...