So the chi square with 1 degree of freedom is the distribution of the variance of the normal distribution? And for n normal variable why It Is a n-1 dof chi square?
You get a pretty complicated distribution because you lose the symmetry in the calculation that comes from the mean being zero for standard normal. I did the calculation. The graph looks similar to a chi-square when mu is close to 0 and sigma is close to 1. On the other hand, when mu gets large, the graph looks more like a normal curve.
Such a great video! It is awesome that you show your complete thought process instead of just giving refined presentation. Extremely comprehensible.
Wish all my students thought that way. Some just want me to tell them what to do as quick as possible.
@@billkinneymath I think learning to think is more important than learning a certain topic 😄
You are indeed a life saver! Thank you so much for that great instructive video.
You're welcome! So glad it was helpful!
Thank you for the video! I appreciate the thorough explanation.
You bet! Thanks for watching!
Super super helpful. Thank you.
You're welcome! Thanks for watching!
You, sir, are a lifesaver.
You're welcome! Thanks for watching!
Wonderful stuff sir !!
Glad you liked it!
Thanks !!!!!!!!!!!!!!!!!!
You're welcome!
So the chi square with 1 degree of freedom is the distribution of the variance of the normal distribution? And for n normal variable why It Is a n-1 dof chi square?
What if the random variable is general normal and not standard normal?
You get a pretty complicated distribution because you lose the symmetry in the calculation that comes from the mean being zero for standard normal. I did the calculation. The graph looks similar to a chi-square when mu is close to 0 and sigma is close to 1. On the other hand, when mu gets large, the graph looks more like a normal curve.