What is a Chi Square Distribution? with examples

Explains the Chi-Square probability distribution and shows two examples where it arises in digital communications.

[Vu-dai-bang]

I love the way you use paper to teach and express things

[黎銘-sn]

I see the beauty of Chi-square distribution now, it a hybrid of variance and central limit theorem. In order to measure disperse of a population variable we square something and in order to see some distributions in aggregate we have sum all up. It's so much fun.

[fasihgardezi]

You are doing a great job. I subscribed to your channel some 5 hours earlier and i have become your fan already. Keep up the good work. And thanks alot

[채명호-wm]

thanks! It is a good vedio.
In your example, does the power of output(y) in a communication channel have two degree of freedom of chai square distribution?

[nickbe]

Thank you sir! Great work as always! I have a question because only one thing is not clear to me: does the chi squared distribution represents the distribution of variance (or variability) of data sample taken from a gaussian distribution? Or It describes the variability of values assumed by X on the abscissa? Because I'm struggling by weeks on this topic. Sorry

[weisanpang]

Hi Sir, pardon my ignorance, normally when a function is squared, the values in the y-axis are squared, in the case of Z being standard normal distribution, I would imagine that the probability values are squared, but in the case of Chi-squared derivation it seemed not. Also, assuming the x axis-values are squared, since the slope of the new curve has changed, does that mean the new probability values from all the squared x-axis values are summed ? I assume the new curve (chi-squared with DF=1) still has area under the curve = 1 ? If chi-squared with DF=1 curve has area under the curve=1, wouldn't adding multiple such curves (i.e chi-squared with DF > 1) result in area under the curve > 1 ? Also by simply adding multiple DF=1 chi-squared curve, how come the shape of the curve changes with different DF ?

[umamaheswarrao]

Good explanation, sir. Can you explain about moment generating function for non-central chi-square
Random variable?

[thepromisedlan]

Thank you for these videos. In the plot for the Chi Squared Distribution, is the X-axis supposed to be x^2 or x?

[tayyabaimran]

very well explained sir.Can you please add a video about distribution of a sum of the squares of k independent standard normal random variables with different variance (Var(z1) != var(z2))

[yourgrace]

The head in the thumbnail looks like skibidi toilet