Correlation of two event indicators

EasyProbability Statistics~3m

Events $A$ and $B$ each have probability $0.5$ , and they co-occur with $P(A\cap B)=0.4$ . What is the correlation between their indicator variables $\mathbf{1}_A,\mathbf{1}_B$ ? Give a decimal to two places.

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Covariance first: $P(A\cap B)-P(A)P(B)$ .
Each indicator's variance is $p(1-p)$ , not $p$ ; divide the covariance by $\sqrt{\operatorname{Var}_A\operatorname{Var}_B}$ .

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0.6 (± 0.001)

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Correlation of two event indicators

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