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  • Hello, folks!

  • 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, calleddegrees of freedom”.

  • We read this next statement asVariable “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 meanmu”.

  • 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!

Hello, folks!

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