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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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# 確率入門。学生のT分布 (Introduction to Probability: Student's T Distribution)

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林宜悉 に公開 2021 年 01 月 14 日