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  • Welcome back, folks!

  • This is going to be a short lecture where we introduce to you the Chi-squared Distribution.

  • For starters, we define a denote a Chi-Squared distribution with the capital Greek letter

  • Chi, squared followed by a parameter “k” depicting the degrees of freedom.

  • Therefore, we read the following asVariable “Y” follows a Chi-Square distribution

  • with 3 degrees of freedom”.

  • Alright!

  • Let's get started!

  • Very few events in real life follow such a distribution.

  • In fact, Chi-Squared is mostly 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 can give you would feel extremely convoluted to anyone not familiar

  • with statistics.

  • Alright!

  • 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 ratherasymmetric.

  • Its graph is highly-skewed to the right.

  • Furthermore, the values depicted on the X-axis start form 0, rather than some 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

  • Student's 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 2 times k.

Welcome back, folks!

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B1 中級

データサイエンスと統計学.カイ二乗分布 (Data Science & Statistics: Chi-Squared Distribution)

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    林宜悉 に公開 2021 年 01 月 14 日
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