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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!

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