Welcome back, folks! This is going to be a short lecture where

we introduce to you the Chi-squared Distribution. For starters, we define a denote a Chi-Squared

distribution with the capital Greek letter Chi, squared followed by a parameter “k”

depicting the degrees of freedom. Therefore, we read the following as “Variable

“Y” follows a Chi-Square distribution with 3 degrees of freedom”. Alright! Let’s get started! Very few events in real life follow such a

distribution. In fact, Chi-Squared is mostly featured in

statistical analysis when doing hypothesis testing and computing confidence intervals. In particular, we most commonly find it when

determining the goodness of fit of categorical values. That is why any example we can give you would

feel extremely convoluted to anyone not familiar with statistics. Alright! Now, let’s explore the graph of the Chi-Squared

distribution. Just by looking at it, you can tell the distribution

is not symmetric, but rather – asymmetric. Its graph is highly-skewed to the right. Furthermore, the values depicted on the X-axis

start form 0, rather than some negative number. This, by the way, shows you yet another transformation. Elevating the Student’s T distribution to

the second power gives us the Chi-squared and vice versa: finding the square root of

the Chi-squared distribution gives us the Student’s T. Great! So, a convenient feature of the Chi-Squared

distribution is that it also contains a table of known values, just like the Normal or Students’–T

distributions. The expected value for any Chi-squared distribution

is equal to its associated degrees of freedom, k. Its variance is equal to two times the degrees

of freedom, or simply 2 times k.

Another great video! Keep them coming, 365!