Original subtitles

Instructor: Welcome back, folks.

This is going to be a short lecture

where we introduce you to the chi-squared distribution.

For starters, we denote a chi-squared distribution

as 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-squared distribution

with three degrees of freedom.

All right, let's get started.

Very few events in real life follow such a distribution.

In fact, chi-squared is most 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 could give you

would feel extremely convoluted

to anyone not familiar with statistics.

All right, 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 from zero rather than a 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 students 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 two times k.

To learn more about hypothesis testing

and confidence intervals,

you can continue with our program where we dive into those.

For now, you know all you need to

about the chi-squared distribution.

Thanks for watching.