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Joint Probability Distribution (Covariation (Concept (Shows how one…
Joint Probability Distribution
Gamma is used for multiple events
Expected Values
Single
\(E(x) = \int{x *f(x)}\)
\(E(x) = \int{h(x) * f(x)}\)
Joint
Covariation
Single
Joint
Concept
Shows how one variable after another
Positive
Increasing X increases Y
proportional
Negative
Increasing X decreases Y
inversely proportional
Neutral
X changing doesn't change Y
Not great for showing how strongly the data is
That is where correlation comes in
Correlation
Concept
Shows how strongly related or weakly related the variables are
[-1,1]
Strong relation means
Even though you can have the same correlation the graphs can vary drastically. Anscombe 's quartet
Independence
Correlation of O doesn't imply independence
Independence however does imply Correlation= O