Hey @karthikeyan_S2,

Welcome, and we are glad that you could become a part of our community

Thanks for creating this thread. I was actually for something like this, since I myself had some confusions in understanding the lecture videos “Law of Large Numbers” and “Central Limit Theorem - Discrete Random Variable”. In my opinion, the videos only serve the purpose of confusing the learners (*be they have some prior knowledge, or be they beginners*).

Let’s begin with discussing the discrepancies in Week 3 (*Lecture 1*), which I have come across till now (*Central Limit Theorem - Discrete Random Variable*):

### Discrepancy 1

- The first lecture video, defines the concept of “sample”, but nowhere in the lecture videos, it has been mentioned that “sample” could mean 2 different things.
- In fact, the lecture videos themselves use “sample” for 2 different meanings.
- “Population and Sample → 0:32”: A sample is a smaller subset that we actually observe or measure (
*Here, it is implying that “sample” refers to the set of samples*) - “Population and Sample → 2:50”: If you thought that the first one was better, that is correct because you always want to take random samples (
*Here, it is implying that “sample” refers to individual samples*)

- “Population and Sample → 0:32”: A sample is a smaller subset that we actually observe or measure (
- Let’s understand it better with the help of an example. Consider the example of a fair dice being rolled. Now let’s say we roll it 4 times, and get
`(1, 5, 4, 2)`

. - Here,
`1`

,`5`

,`4`

and`2`

are individually referred to as samples. But the confusing part is that`(1, 5, 4, 2)`

in itself is also referred to as a sample. - Say, if we roll the dice for 4 more times, and let’s say we get
`(2, 6, 3, 1)`

. Here, this is another sample, consisting of 4 samples. - Therefore, for our discussion, we have 2 samples, each consisting of 4 samples, i.e., we have a sample-size of 4.
- For reference, check out this video, time-stamp 2:10 onwards. Unlike Luis, Sal has explicitly mentioned this.

### Discrepancy 2

- In the Coursera videos, the same notation has been used for different concepts in different videos.
- Now, off course, we can use the same variable to denote different things, after all, they are variables
- But I believe that the important parameters should always be denoted with different variables, and the notation should be consistent throughout the videos.
- You will find that in the lecture videos “n” denotes both sample-size, as well as the number of samples. I am mentioning 2 references here:
- “Population and Sample → 2:03”: In this example, the population size is 10,000, denoted by N, and the sample size could be anything smaller, from 1-9,999, that’s denoted by n (
*Here, n denotes sample size*) - “Law of Large Numbers → 2:32”: So if n is the number of samples (
*Here, n denotes number of samples*)

- “Population and Sample → 2:03”: In this example, the population size is 10,000, denoted by N, and the sample size could be anything smaller, from 1-9,999, that’s denoted by n (

## Conclusion

- These are the 2 major discrepancies which I could observe as of now, and a lot of minor discrepancies, and in my opinion, these make the videos more confusing than they make them beneficial for the learners.
- In fact, you are not the first one to feel that the videos are confusing or incorrect. Check out the following threads: Thread 1 and Thread 2.
- At this, point I would suggest you to follow other content on the web, since the team is still working on fixing the content. For starters, you can check out this playlist, which I believe is an amazing source of knowledge.

P.S. - @lucas.coutinho please take a note of this thread. Currently, the content of Week 3, Lecture 1 is extremely confusing, and needs some major changes on an urgent basis. I guess, adding a note regarding this can be helpful for the learners, so that they can avoid getting confused meanwhile.

Cheers,

Elemento