Deriving a Confidence Interval for a Variance (Assuming a Normally Distributed Population)

I derive the appropriate formula for a confidence interval for a population variance (when we are sampling from a normally distributed population). I do not do any calculations or look at any examples in this video, I simply derive the appropriate confidence interval formula.
I work through an example at / tslgbpu \NPk

[@htchtc203]

Thank you Sir. Your presentation was very clear and help to understand how the limits are derived.
Sir, does the same derivation apply for Rayleigh distribution.
Sir, I hope you would elaborate WHY the sample variance follows the chi square distribution.

[@alexxela8192]

I like all your tutorials. One question: where this (n-1)s^2/sigma^2 comes from?

[@anilthapa1931]

It is studied as a theorem in chi-square distribution. Given a random sample X1, X2,..., Xn. from a population X with normal distribution then (n-1) s^2/sigma^2 will have a chi-square distribution with n-1 degree of freedom), where s is sample variance and sigma is population variance.

[@stefanofedele4820]

Long story short we saw that
- the distribution of the average of a random variable with a generic distribution function is well approximated by the Gaussian (central limit theorem)
- while the distribution of the variance of a normally distributed variable (such as the average from the sampling on a generic random variable) is well approximated by the chi squared distribution function.
This last assumption allows us to estimate the interval of confidence once we decided which is the probability we choose to define "success" and "failure"

[@asolisca]

Hello! What software do you use to create the graphs?! They're amazing! Congrats!

[@brianterry8775]

This cleared up a gap in my lecture notes - thanks! :)

[@haniasyoutubechannel3742]

Very much well explained....thanks sir

[@roseb2105]

I get it that for a regular mean of data sets 12345 we take each number to see how far it is from the average but with proportion we are just counting the number of people that say yes out of the total number of respondents so what does the variance mean in this case?

[@saulgoodalvarez]

Very well explained, sir. Thank you very much!

[@lihlewelani6892]

How would you construct a 100(1-alpha)% in upper and lower confidence bound for variance?

[@jbstatistics]

I work through an example of that here: ruclips.net/video/qwqB5a7_W44/видео.html&ab_channel=jbstatistics

[@roseb2105]

can somone please explain what does it mean a variance of a proportion and the formula// for this ???//////

[@rf7256]

variance of a proportion is the same as saying the sample variance. its the variance of a proportion of the population. sample variance= 1/(n-1)* [sum of (Xi-Xbar) from i=1 to n]

[@AbrarAhmed10]

Thank you so much sir, your videos help me a lot.

[@jbstatistics]

+Abrar Ahmed You are very welcome. All the best!