No more car videos or car books for just a second. I mean, they’re great. They’re interesting, but no more, at least for two books and then we’ll go back to finishing it up, four more car books. It’s going to be a whole series, the car books.
So we got an Introduction to Probability and Statistics.
We’ve got probability, random variables in there, probability distributions moments in generating functions, multiple random variables, some special distributions limit theorems, samples.
A whole bunch of stuff. But however, let’s look at what is probability? I’ll give you a quick little introduction on there and then random variables in our probability distributions. So we’re going to do a little bit on page 1 in a little bit on page 40. So don’t let me forget. So page UNO.
Okay. The theory of probability had its origin in gambling and games of chance. This is part of the reason why I was like probability. You guys might not know, but if you’re a degenerate, like I am like the gamble or like the stock market then probabilities is really important for you. [inaudible 00:01:48] in gambling and games of chance, it owes much of the curiosity of gamblers who pestered their friends in the mathematical world with all sorts of questions. Unfortunately, this association with gambling contributed to a very slow and sporadic growth of probability theory as a mathematical discipline. The mathematicians of the day took little or no interest in the development of any theory, but looked only at the combinational reasoning involved in each problem. The first attempt at some mathematical rigor is credited to Laplace.
In his monumental work, Theorie analytique des probabilities, so he is Latin or French. I would say that’s more Latin, in 1812. Laplace gave the classical definition of the probability of an event that can occur only in a finite number of ways as a proportion of the number of favorable outcomes to the total number of all possible outcomes, provided that all the outcomes are equally likely. According to this definition, computation of the probability events was reduced to combinatorial counting problems. Even in those today, this definition was found inadequate in addition to being circular and restrictive, it did not answer the question of what probability is. It only gave a practical method of computing, the probabilities of some simple events, all right.
But he did pretty good for 1812, right? And to think it’s even saying that games of chance and gambling was the origin of probability. The first person that came up with thinking of probability was in 1812, right? So gambling and gaming games of chance has been around for a very long time in trying to find out the probability. So, like I said, I’m going to go more into this, but I want to get into 42. And I don’t want these videos to be too long. Right.
Probability for kind of what he was talking about. What is the chances of something happening? If everything is the same, right? So in cards you can count the probability. If you know how many sets, how many cards are. There’s 52 cards is 13 per color or symbol, right? So when you have that finite amount of numbers you can count and you can do mathematical equations. You can figure out the probability of something happening next, right? With the stock market, there’s a million different variables, but in all actuality, there’s only like five or six things that somebody can do. It can go up, it can stay the same, or it can go down right as three things. However, it can go up slow, fast. That’s two. It can stay the same violently or very calm. So either volatile or not volatile, or it can go down very fast or very slow. So off of three things. You have actual six things right now. There’s volume, there’s variables, there’s times of the year. There’s all these different variables. But in all essence, there’s only six things that this can do. It can stay the same. It can go up, it can go down, it can stay the same peacefully. It can stay the same violently. It can go up fast. It can go up slow. It can go down. Slope can go down fast, right? So it’s probable, it’s going to do something now with all the different variables and everything you can calculate using calculations. And then you can come up with formulas and everything to better hypothesize which direction or what it’s going to do. But in the same, you have six different possibilities for it to do, right? I didn’t know all those different variables. Now you have your probabilities now. Now, 40.
Random variables and their probability distributions. Right? And in chapter one, we dealt essentially with random experiments that can be described by, okay, no random variables where does exist. We defined a random variable. And in study two, three, we study the notion of probability distribution of a random vehicle variable. No, just what is a random, okay. Actually in chapter one, we were concerned with such functions without defining term random variable. Here we study the notion of random variable and examine random variables’. In chapter one, we study probabilities of a set function P defined on a sample space. Rome.
I can’t remember what those signals saying. I’ll just show you. You can figure it out. Those two, since P is a set function, it is not easy to handle. We cannot perform arithmetic or algebraic operations on sets more note, moreover in practice one frequently observed some function of elementary events. When a coin is tossed repeatedly, which replication resulted in heads is not of much interest. Rather, one is interested in the number of heads and consequently, the number of tails that appear in, say, N tossings of the coin. It is therefore desirable to introduce a point function on the sample space when we can then use knowledge or calculus or real analysis to study properties of P .
So then we get into a whole bunch of, yeah, baby. Excited to learn a whole bunch of gibberish, right? I mean, it’s not, sorry. Shanaya said it’s gibberish. It might be more advanced for my feeble mind that I have over here because this is a lot of numbers. I don’t know what they mean. This is the introduction. What’s the second part. What I’m saying, this is level one. What’s level five. Look like a whole bunch of gibberish I’ll never understand.
Yes, I will try to decipher as much as the first. What is probability and why is it important? And I will try to decipher as much as the little, the equations as possible. Don’t make very many promises, but I will do my best to make it nice and simple for you to understand in the essay. All right, done with that one. Almost done with this box, man, almost done with this box. This box was massive.