I am following George G Roussas's book An Intro to prob and stat inf (2nd ed). At 24:50 the way you write sigma square hat, i.e. 1/n sum_{1}^n(xi - x bar)^2 = (1-1/n) S_{n}^{2} .. Roussas in page 296 at exercise 1.12 part (iv), writes 1/n sum_{1}^n(xi - x bar)^2 = Sx .. which notation is correct ?
Usually the accepted convention is for the sample variance to use a denominator of (n-1) rather than n. This is because using a denominator of (n-1) gives an unbiased estimator. That is, E(S_n^2)=sigma^2. That being said, some textbooks will define it differently depending on the context.
as it is a common term, we take the 1/sigma^2 to the right side and it becomes zero. You can keep the sigma^2 but during calculation, you would be able to see that it would be canceled from both sides. So both methods are actually the same.😊😊
first he rescaled the gaussian integral and distributed the exponent within the exp function, then on the term outside the integral he made sigma = sigma^2 ^.5
I'm pretty sure this is that video. normal distribution is a rescaled gaussian integral so that the area under the curve is 1, making it a pdf. gaussian distribution and normal distribution is the same thing
bravo. you explained what my professor took in 6 hours to explain in 6 minutes. thank you 🙏
Excellent Lecture
Thankssss,i understood every step in all the videos you made unlike in class.Bless you
28:49 why do we have to show that second condition is positive? Does it have to do woth the determinant of hessian matrix or whatever its called
Appreciated much your explanation! ❤️
I am following George G Roussas's book An Intro to prob and stat inf (2nd ed).
At 24:50 the way you write sigma square hat, i.e. 1/n sum_{1}^n(xi - x bar)^2 = (1-1/n) S_{n}^{2} .. Roussas in page 296 at exercise 1.12 part (iv), writes 1/n sum_{1}^n(xi - x bar)^2 = Sx .. which notation is correct ?
Usually the accepted convention is for the sample variance to use a denominator of (n-1) rather than n. This is because using a denominator of (n-1) gives an unbiased estimator. That is, E(S_n^2)=sigma^2. That being said, some textbooks will define it differently depending on the context.
Amazing, thank you so much for these derivations.
thaks for your explanation, very clear. your video helped me to solve my HM :))
superb
15:44 haha! Ypu are such a charming person... Love you!
I'm wondering what happened at 21:30, the 1/sigma^2 is gone.
as it is a common term, we take the 1/sigma^2 to the right side and it becomes zero. You can keep the sigma^2 but during calculation, you would be able to see that it would be canceled from both sides. So both methods are actually the same.😊😊
yeah i realized like thirty seconds later ican multiple both sidess xD @@shashadhikary2298 this comment looks stupid now
Hi, thanks for video. It was fantastic, especially as u have shown all the steps.
I am wondering which app have u used for the writing?
great explanation! i just think there's a correction in terms of notation for the last part, MLE of sigma^2 is sigma^2_hat (not sigma_hat). :)
Thanks for this very clear explanations
Hi Samuel Cirrito-Prince, thank you for this great video, but i am curious how the sigma in the pdf definition became sigma^2
first he rescaled the gaussian integral and distributed the exponent within the exp function, then on the term outside the integral he made sigma = sigma^2 ^.5
Is there any about mle of hmm?with gaussian distribution?
I'm pretty sure this is that video. normal distribution is a rescaled gaussian integral so that the area under the curve is 1, making it a pdf. gaussian distribution and normal distribution is the same thing
thank you
Thanks
not a shit explanation for once! Rare to see.
Explain the concept of likelihood not example.
it better shown in an example smh, this guy did a great job