Quadratic Formula | You won't forget how to solve it after this video

Quadratic Formula | You won't forget how to solve it after this video

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What is Randomness

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Randomness is one of the most important pillars to support the statistic and probability temple.  Randomness is unpredictable. In the common parlance, randomness is the apparent lack of pattern or predictability in events. Please remember: Randomness is unpredictable but it not equal to uncertainty. Let’s say team A has a 60 percent chance to win the game, that percentage is a certain number although you can’t tell whether they will win or lose next time. We can consider randomness is that we know all the possibilities, the only thing we don’t know is which one will happen next. Flipping a coin, you don’t know whether it will show head or tail, but it must be one of them. Shuffle play music, although you can’t predict which song will play next, it must be one on your playlist.  On the other hand, uncertainty is we have no idea what can happen next. For example the Black swan theory - something that comes as a total surprise. Bay the way all swans in New Zealand are black, here’s a pi
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Quantify probability

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We finally come to the last foundation of statistics and probability. Quantify probability. If I said, my favorite team more likely to win the next game you probably feel that is a vague  statement. I can do it better: my favorite team has an 80% chance to win the next game. How to come to that percentage? Well, you may think it must be very complex and even unachievable. Actually, there are only three principles when quantifying the probability. Permutation and combination method: let us see an example. What is the probability of a rolling dice stop showing 6? There are 6 positions the dice may end up: 1 2 3 4 5 6. 6 is one of them. So that the chance of getting 6 is 1to 6. The key to quantifying probability using the permutation and combination method is finding all possible outcomes. we can use permutation and combination to deal with a single random event but what if there are multi random events? Sum method: when calculating the chance of a happens or b happens we can sum each pro
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Law of large numbers

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Frequentist makes it possible to forecast the probability of a future event based on the current frequency. Frequentist works because of the law of large numbers. There are two different versions of the law of large numbers: the weak law of large numbers and the strong law of large numbers. In 1713, Swiss mathematician Jakob Bernoulli after 20 years of hard work proved that (if you have a sample of independent and identically distributed random variables, as the sample size grows larger, the sample mean will tend toward the population mean.) the sample average converges in probability towards the expected value This known as the Weak Law of Large Numbers or Bernoulli's theorem. It tells us as more trails performed the frequency will more likely to become closer to the true probability. Be aware that it is only more likely not a 100% guarantee. Bernoulli’s theorem gives us confidence that a random event has a great chance to have a certain probability. In 1930 Andrey Kolmogorov pro
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