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proux01 committed Sep 23, 2023
1 parent 812c17d commit 9490ab2
Showing 1 changed file with 4 additions and 3 deletions.
7 changes: 4 additions & 3 deletions theories/probability.v
Original file line number Diff line number Diff line change
Expand Up @@ -489,10 +489,11 @@ rewrite lee_sqrE ?sqrte_ge0// sqr_sqrte ?mule_ge0 ?variance_ge0//.
rewrite -(fineK (variance_fin_num X1 X2)) -(fineK (variance_fin_num Y1 Y2)).
rewrite -(fineK (covariance_fin_num X1 Y1 XY1)).
rewrite -EFin_expe -EFinM lee_fin -(@ler_pM2l _ 4) ?ltr0n// [leRHS]mulrA.
rewrite [in leLHS](_ : 4 = 2 * 2)%R -natrM// natrM mulrACA -expr2 -subr_le0.
apply: deg_le2_ge0 => r; rewrite -lee_fin !EFinD.
rewrite [in leLHS](_ : 4 = 2 * 2)%R -natrM// [in leLHS]natrM mulrACA -expr2.
rewrite -subr_le0; apply: deg_le2_ge0 => r; rewrite -lee_fin !EFinD.
rewrite EFinM fineK ?variance_fin_num// muleC -varianceZ//.
rewrite -mulrA EFinM mulrC EFinM ?fineK ?covariance_fin_num// -covarianceZl//.
rewrite 2!EFinM ?fineK ?variance_fin_num// ?covariance_fin_num//.
rewrite -muleA [_ * r%:E]muleC -covarianceZl//.
rewrite addeAC -varianceD ?variance_ge0//=.
- by rewrite compre_scale ?integrableZl.
- rewrite [X in EFin \o X](_ : _ = r ^+2 \o* X ^+ 2)%R 1?mulrACA//.
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