Mathematics, 11.03.2020 04:26, taytay210
Let A be an event, and let IA be the associated indicator random variable ( IA is 1 if A occurs, and zero if A does not occur). Similarly, let IT be the indicator of another event, B . Suppose that P(A)=p , P(B)=q , and P(A∩B)=r . Find the variance of IA−IB , in terms of p , q , r . Var(IA−IB)=
Answers: 3
![var(IA) = E(IA)^2 - [E(IA)]^2\\=I^2\dot P(A) + 0^2(I-P(A))-[1P(A)+0(I-P(A))]^2\\=P(A)+0-[P(A)+0]^2\\=P(A)-[P(A)]^2\\=P(A)[1-P(A)]](/tpl/images/0542/4317/0a351.png)
![P[1-P]\\\therefore\, var(IA)=P[1-P]...(1)](/tpl/images/0542/4317/cc120.png)
![cov(IA,\, IB)=E(IA\dot IB)-E(IA)E(IB)\\=1\times P(AnB)+[0times P(AnB)^c]-P\times q](/tpl/images/0542/4317/c9dbb.png)
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Let A be an event, and let IA be the associated indicator random variable ( IA is 1 if A occurs, and...
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