In this lesson we are going to talk about the Students' T distribution and its characteristics.

Before we begin, we use the lower-case letter “t” to define a Students' T distribution,

followed by a single parameter in parenthesis, called “degrees of freedom”.

We read this next statement as “Variable “Y” follows a Students' T distribution

with 3 degrees of freedom”.

As we mentioned in the last video, it is a small sample size approximation of a Normal

Distribution.

In instances, where we would assume a Normal distribution were it not for the limited number

of observations, we use the Students' T distribution.

For instance, the average lap times for the entire season of a Formula 1 race follow a

Normal Distribution, but the lap times for the first lap of the Monaco Grand Prix would

follow a Students' T distribution.

Now, the curve of the students' T distribution is also bell-shaped and symmetric.

However, it has fatter tails to accommodate the occurrence of values far away from the

mean.

That is because if such a value features in our limited data, it would be representing

a bigger part of the total.

Another key difference between the Students' T Distribution and the Normal one is that

apart from the mean and variance, we must also define the degrees of freedom for the

distribution.

Great job!

As long as we have at least 2 degrees of freedom, the expected value of a t-distribution is

the mean “mu”.

Furthermore, the variance of the distribution equals: the variance of the sample, times

number of degrees of freedom over, degrees of freedom minus two.

Overall the Students' T distribution is frequently used when conducting statistical

analysis.

It plays a major role when we want to do hypothesis testing with limited data, since we also have

a table summarizing the most important values of its CDF.

Great!

Another distribution that is commonly used in statistical analysis is the Chi-squared

Distribution.

In the next video we will explore when we use it and what other distributions it is

related to.

Thanks for watching!