Hi, many thanks for your comment. Glad to hear you found it useful. I do intend to make more videos on the more pure statistical theory, alhough I fear it may not be in time for your exam unfortunately. Good luck with the exam, and please let me know any further additions you think would be useful.Thanks, Ben
Amazing lectures, these help me alot. I will have exam next tuesday and you make SENSE! Keep working on these videos, maybe some more examples with higher difficulty.
In the property part, you are talking about group of independent random variables. Do you mean if we add up these random variables? Because this very looks like the CF of the sum of those random variables.
The formula for the characteristic function is E[e^(itx)], while the formula for the moment generating function is E[e^(tx)]. Why is there a difference (the i)?
Hi, thanks for your message. Yes - it appears quite a subtle difference. However, it does make a significant difference to the sort of function which results. The reason being that when we include i, it is necessary to evaluate an integrand in the complex plane. It is possible to show that for any random variable a CF always exists whereas this is not necessarily the case for a MGF. Hope that helps. Best, Ben
Hi, many thanks for your comment. Glad to hear you found it useful. I do intend to make more videos on the more pure statistical theory, alhough I fear it may not be in time for your exam unfortunately. Good luck with the exam, and please let me know any further additions you think would be useful.Thanks, Ben
Amazing lectures, these help me alot. I will have exam next tuesday and you make SENSE! Keep working on these videos, maybe some more examples with higher difficulty.
Nice introduction to the topic.
Very clear explanation! Thanks for posting this video!
In the property part, you are talking about group of independent random variables. Do you mean if we add up these random variables?
Because this very looks like the CF of the sum of those random variables.
Hi, thanks for your message. Yes I am talking (I can see it wasn't very clear here) about the sum of random variables. Best, Ben
@@SpartacanUsuals m
Thank you for making these videos
The formula for the characteristic function is E[e^(itx)], while the formula for the moment generating function is E[e^(tx)]. Why is there a difference (the i)?
Hi, thanks for your message. Yes - it appears quite a subtle difference. However, it does make a significant difference to the sort of function which results. The reason being that when we include i, it is necessary to evaluate an integrand in the complex plane. It is possible to show that for any random variable a CF always exists whereas this is not necessarily the case for a MGF. Hope that helps. Best, Ben
+Ben Lambert
? does it the same function which was introduced by Harmsen for the detection of steganography
Love the videos. Do you prove the one to one mapping in any of your videos?
How’s life
For the second property relating to "ax", shouldn't "ax" be the domain of probability distribution? Like (e^itax)P(ax)dx
You're right but P(ax) is always identical to P(x) for any non-trivial constant (i.e. a not equal to 0).
Very Nice. Thank you very much.
Great vid !
Tq so much prof
Does the t here stand for time?
Thank you sir
You sounded like simon
SORT OF