3. Probability Theory

MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
Instructor: Choongbum Lee

This lecture is a review of the probability theory needed for the course, including random variables, probability distributions, and the Central Limit Theorem.

*NOTE: Lecture 4 was not recorded.

License: Creative Commons BY-NC-SA

[SeikoVanPaath]

Some notable Timestamps:
0:01:20 Random Variable (RV)
0:05:06 Probability & Expectation
0:09:01 Normal Distribution
0:25:32 Other Distributions
0:32:30 Moment Generating Function
0:48:00 Law of Large Numbers
1:04:00 Central Limit Theorem

[haashirashraf]

It's amazing that this is for free, teaching done the right way whether your a high school kid looking for some deeper knowledge or even a college freshman trying to fully comprehend the basics or someone simply recapping basic probability theory, this video serves all purposes to some extent.

[abdelrahmangamalmahdy]

thanks for continuing uploading complete courses for free

[whatitmeans]

I think is more accurate to understand why Gaussian distribution is so universal because it is the maximum entropy distribution for a finite mean and variance, in simpler words, is the most dissordered possible scenario for a proccess with finite energy. It tells you that all information of the events is already lost, as example, like knowing the falling path of a ball in the Galton's board from the slot it have fallen. The lobe-like shape could be explained due concentration inequalities like Markov's.

[joshschwartz]

Thank you for the video. Just a note: you need to evaluate the moment generating function at t=0 after differentiating in order to get the k-th moment. It was implied, but not said. Thanks again!

[alexpan]

two years ago, i could not understand at all because of my poor background, now i can follow due to my hard work on probability and statistics. Mr. Lee is awesome! Thanks for providing us with so good lectures!

[woodypham]

This lecturer deliver a pain killer pill
to students who used to be struggling to understand random walk and probability theory.

[youngseokjeon]

at 38:52, i think the derivative should be evalutated at t=0 to produce the desired expectation value.

[billdu]

Shouldn't the expression at 14:04 be (P[n] - P[n-1])/P[n-1] ?

[MLirola]

Watching it in 2024
Loving every minute.
Thank you for sharing this kind of content for free.

[mohammadaljarrah]

In 2:38 it is not true that the p.m.f be a function from \Omega(sample space) to R+, the true is the p.m.f fX is a function from R to [0, 1]. In fact the random variable X is a function from \Omega(sample space) to R, and the p.m.f fX associate to X is defined as fX(x) = P(s in \Omega | X(s)=x)

[albertrombone]

What is this guy experience with poker? We want to know more!

[georgbraun]

There's an error at minute 10 - sigma^2 is the variance. sigma is the standard deviation.

[forKyrene]

2:05 Shouldn't it be Probability Density Function for continuous random variables? Or is probability density function the same as probability distribution function? As far as I know (correct if I'm right), probability mass function (discrete) and probability density function (continuous) are both probability distribution functions.

[Vamavid]

The only reason I understand this is I've done it before. I guess this means that MIT grads aren't smart because they went to MIT, they had to be smart to be allowed in!

[DF-edjj]

There's something wrong at the beginning of the lecture. A random variable is a function from the sample space to R, that is X: omega --> R.

Here's the guy said that are the pmf and pdf of a r.v. to take values from the sample space into R, which is uncorrect.

[IVVIIVVII]

topppp. this lecture helps to understand probability logically by making theoretical ideas more sensible. def a battle all the way through. haha.

[AdityaRaj-ktew]

To model the stock market, it is more reasonable to assert that the rate
of change of the stock price has normal distribution (compared to the stock
price itself having normal distribution).


I don't understand why so?

[johanneswestman]

If there's one thing that I learned in my engineering classes it is that theorems are fun and all but practically useless unless you're doing research. Monkey see, monkey do. Examples > all.

[mateotinoco]

Not everything, MIT produces is high quality...like this lecture. I guess they don't have enough money for a projector, a TV or powerpoint