Original subtitles

-: Hello folks.

In this lesson, we are going to talk

about the student's T distribution and its characteristics.

Before we begin, we use the lowercase letter T

to define a student's T distribution,

followed by a single parameter in parenthesis,

called degrees of freedom.

We read this next statement

as variable Y follows a student's T distribution

with three 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 student's T distribution.

For instance, the average lap times for the entire season

of a Formula One race follow a normal distribution.

But the lap times for the first lap

of the Monaco Grand Prix would follow

a student's T distribution.

Now, the curve of the student's 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 student's 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 two 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 the number of degrees of freedom,

over degrees of freedom minus two.

Overall, the student's 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 where we use it,

and what other distributions it is related to.

Thanks for watching.