Not only was this video really helpful, but the way that you organize the related topics and link them below your videos is very helpful in connecting students to the full background needed to understand a topic. Thank you!
I have been studying the c.f. for the last two days and I'm finding It very intresting. The most intresting part for me was the inverse theorem, the one where you show that the distribuiton function can be written trought a limit containing the c.f.
One of the reasons it's considered is because it makes the calculation of the pdf of the sum of random variables easier to calculate (as explained in the video). That's a good reason. But I don't think there is a physical interpretation, sorry.
The expectation on the top right hand side of the page only separates into the two seperate characteristic functions when the random variables are independent. But the characteristic function can still be useful for analysing dependent variables - it just doesn't seperate so nicely, that's all.
While I'm grateful for your overviews, I can't help but think that an actual, practical worked example rather than an abstract one would be much more helpful in understanding the application.
Good point. Yes, I always think examples help. But I also think that the fundamental definitions are also important, and it's not always easy to fit both into a single short video. I'll add an example to my "to do" list for a future video. Thanks for the suggestion.
Not only was this video really helpful, but the way that you organize the related topics and link them below your videos is very helpful in connecting students to the full background needed to understand a topic. Thank you!
I'm glad you like the approach, and the videos too. It's great to know they're useful.
Thank u very much man. Your channel is highly undervalued
Glad you found it useful.
This is pure gold. Thank you so much for this video!
You're so welcome!
Your presentation is very simple, short and easy to grasp. I have understood many concepts from your videos. Thanks indeed.
I'm really glad to hear it. Thanks for letting me know.
Perfect. Simply put together.
I'm so glad you liked it.
I have been studying the c.f. for the last two days and I'm finding It very intresting. The most intresting part for me was the inverse theorem, the one where you show that the distribuiton function can be written trought a limit containing the c.f.
I'm glad to hear the video was helpful.
Crystal clear explanation, thank you!
Glad it was helpful!
Thank you so much :)
Glad it helped!
Very helpful. Thanks.
Glad it was helpful!
What is the physical interpretation of characteristic function. Why expectation of complex exponent of random variable is considered.
One of the reasons it's considered is because it makes the calculation of the pdf of the sum of random variables easier to calculate (as explained in the video). That's a good reason. But I don't think there is a physical interpretation, sorry.
Sir/Madam ...Can you derive Mean of Uniform RV from its characteristic function....? Please post the video
Thank you so much.
You're welcome!
Does this result ever hold if Z = X + Y but X and Y are not independent ?
The expectation on the top right hand side of the page only separates into the two seperate characteristic functions when the random variables are independent. But the characteristic function can still be useful for analysing dependent variables - it just doesn't seperate so nicely, that's all.
While I'm grateful for your overviews, I can't help but think that an actual, practical worked example rather than an abstract one would be much more helpful in understanding the application.
Good point. Yes, I always think examples help. But I also think that the fundamental definitions are also important, and it's not always easy to fit both into a single short video. I'll add an example to my "to do" list for a future video. Thanks for the suggestion.
Thank you
You're welcome
Watching it the day before exam 🙂
Good luck on your exam!
@@iain_explains it went well
Great to hear.
Watching one day before exams ☺️
It's never too late! I hope your exams went well.