Understanding Expected Values and Covariance in Probability and Statistics
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1) E(???????? + ????) = ∑ (???????????? + ????)????(???? = ????????) 2)
????????????
(????) = ????[(???? − ????͓)² ]
= ∑ ????????????????(???? = ????????) + ∑ ????????(???? = ????????) =????[????²+(????͓)²− 2????͓ ????]
= ????∑ ????????????(???? = ????????) + ???? ∑ ????(???? = ????????)
=????[????]²+????͓²− 2????͓ ????[????]
= ????????(????) + ????
=????[????]²−????͓²
= ???????????? + c
3) ????????????(???????? + ????) = ????{[(???????? + ????) − (a????͓ + ????)]²} 6) ????????????(????, ????)
= ????{[????(???? − ????͓)] ²}
=????[(????– ????͓)(???? − ????͓)]
=????² ????[(... Continue reading "Understanding Expected Values and Covariance in Probability and Statistics" »